Venus(vē´nus); called by the GreeksAphrodite(af-ro-dī´tē)—i. e.“sea-foam.”—The goddess of love and beauty. She was supposed to have sprung from the foam of the sea: hence her Greek name. She was the wife of Vulcan, but was very unfaithful to him. She loved the gods Mars, Bacchus, Neptune and Mercury, and the mortals Adonis and Anchises. She was considered byParis(q.v.) the most beautiful of the goddesses and had awarded to her the celebrated Golden Apple. Anyone who wore her magic girdle immediately became beautiful and the object of love and desire. She is generally accompanied by her son Cupid. The month of April, as the commencement of spring, was considered peculiarly sacred to the goddess of love. The myrtle, rose, apple and poppy, and the sparrow, dove, swan and swallow, were all sacred to her. She was probably originally identical with Astarte, a Syrian goddess, called by the Hebrews Ashtoreth. As might have been anticipated, the representation of the Queen of Beauty on canvas and in marble has resulted in some of the finest works of the most celebrated painters and sculptors of antiquity. Among the former, Apelles’ masterpiece of Venus rising from the sea deserves special mention; and among the latter the “Cnidian Venus” (so called because it stood in her temple at Cnidus), by Praxiteles, is unquestionably the most famous. Phryne (q.v.) sat as model for both of these noble works of art. The fame of the “Cnidian Venus” was so great that travelers from all parts of the civilized world resorted to Cnidus in order to see it. In fact, Pliny and others declared it to be the finest statue in the world. The “Venus of Milo” is, however, the noblest extant representation of Venus. It was found, in 1820, in the island of Melos, the modern Milo (hence the epithet), which is one of the group of islands named the Cyclades, in the Ægean Sea. It now forms one of the treasures of the Louvre, Paris.
Vertumnus(ver-tum´nus).—The god of the changing year—that is, of the seasons and their productions. His festival was celebrated by the whole Roman people on the 23rd of August.
Vesta(ves´ta); called by the GreeksHestia(hes´ti-a)—i. e.“the hearth.”—One of the twelve great Roman deities, the goddess and guardian of the hearth and home. She was the daughter of Saturn and Rhea. In her temple in the Forum at Rome stood no statue, the goddess being represented by the eternal fire burning on her altar as her abiding symbol. This fire was kept up and attended to by a number of virgin priestesses, called Vestals, who were chaste and pure like the goddess herself. On March 1 in every year the sacred fire was renewed, and on June 15 her temple was cleaned and purified.
Vidar.—The Scandinavian god of wisdom, noted for his thick shoes, and not infrequently called “The god with the thick shoes.”
Vishnu.—In Hindu mythology one of the great deities of the Hindu triad, ranking as thePreserver, after Brahma, theCreator, and before Siva, theDestroyer. It is believed that he has appeared on earth nine times, his tenthavatar, or incarnation, having yet to come.
Volumnia(vol-um´ni-a).—Wife ofCoriolanus(q.v.).
Vulcanus(vul-kā´nus), orVulcan; calledHephæstus(hē-fēs´tus) by the Greeks. The god of fire. He was the son of Jupiter and Juno, and was lame from his birth. Besides being the god of fire, he was master of the arts which need the aid of fire, especially of working in metal. He made all the palaces of the gods on Olympus, the armor of Achilles, the fatal necklace of Harmonia, the fire-breathing and brazen-hoofed bulls of Æëtes (see “Argonautæ”), etc. The Cyclops were his workmen, and his workshops were situated under Mount Ætna in Sicily. Vulcan’s wife was Venus. His favorite abode on the earth was the island of Lemnos. His great festival was celebrated on the 23rd of August.
W
White Lady.—In German folk-lore, the ancient Teutonic goddess Holda or Berchta, who was the receiver of the souls of maidens and children, and who still exists as the White Lady, not infrequently, in German legends, transforming herself, or those whom she decoys into her home, into a white mouse.
Wild Huntsman, The.—A spectral hunter in folk-lore, especially in German folk-lore; the subject of a ballad by Bürger.
Woden(wō´den), orWotan.—The Anglo-Saxon form of the Scandinavian god Odin; Wednesday is called after him.
Y
Yama.—In theRigveda, the name of the god who rules in heaven over the blessed—the Manes, Fathers, or Pitris—and is therefore called king.
Yggdrasil.—In Scandinavian mythology the great ash tree which binds together heaven, earth, and hell. Its branches extend over the whole earth, its top reaches heaven, and its roots hell. The three nornas, or fates, sit under the tree, spinning the events of man’s life.
Z
Zem.—The sacred well of Mecca. According to Arab tradition, this is the very well that was shown to Hagar when with Ishmael in the desert. It is supposed to be in the heart of the city of Mecca.
Zephyrus(zef´i-rus).—The west wind, or properly, the northwest.
Zeus(zūs).—See “Jupiter.”
Zohak.—The giant of Persian mythology who keeps the “mouth of hell.” He was the fifth of the Pischdadian dynasty, and was a lineal descendant of Shedâd, king of Ad. He murdered his predecessor, and invented both flaying men alive and killing them by crucifixion. The devil kissed him on the shoulders, and immediately two serpents grew out of his back and fed constantly upon him. He was dethroned by the famous blacksmith of Ispahan, and appointed by the devil to keep hell-gate.
Zohara.—An oriental queen of love, and mother of mischief. When Harût and Marût were selected by the host of heaven to be judges on earth, they judged righteous judgment till Zohara, in the shape of a lovely woman, appeared before them with her complaint. They then both fell in love with her and tried to corrupt her, but she flew from them to heaven; and the two angel-judges were forever shut out.
Zulzul.—According to Chinese mythology the sage whose life was saved in the form of a rat by Gedy, the youngest of the four sons of Corcud. Zulzul gave him, in gratitude, two poniards, by the help of which he could climb the highest tree or most inaccessible castle.
The relationship of these mythical personages are quite unlike those of mortals and are full of inconsistencies. To reconcile all the contradictions of the poets and mythologists is impossible. Perhaps this chart is as consistent with their fabulous tales as can well be made.
CHAOSProducedEREBUS, god ofdarkness, NOX, goddess ofnight, and TERRA,Earth.-TITANOldest of the twelve Titans.--JUNO, wife and sister of Jupiter, queen of the gods, and of Heaven and Earth.-By Them´is.Astræa, the goddess ofjustice;Nemesis, ofvengeance.By Juno.Mars, the god ofwar; byVenus, Anteros, Harmonia; the goddess ofyouth; once cupbearer to Jupiter.THE CYCLOPSGiants, at first three in number:Arges,Brontes,Steropes.JUPITERorZeus, the most powerful of all the gods; king of gods and men, hadHebe, by her husbandHercules, Alexiares and Anicetus.Typhon, by the monsterEchidna, Chimæra and Sphinx.Vulcan, the god offireand ofblacksmiths, and husband of Venus; by his wifeVenus, Cupid; byMedusa, Cacus, byJuno, Cæculus.By Lato´na.Apollo, the god ofpoetry,music,eloquence,medicine,the fine arts,augury, andarchery.Diana, the goddess ofhunting, the patroness of chastity, presided also over childbirth.By Ma´ia.TERRA or TITÆAproducedCŒLUSor URANUS,Heaven.BRIAREUSA famous giant called by men Ægæon, and by the gods Braireus.Mercury, themessengerof the gods, the god ofeloquenceandcommerce, the patron oftravellers,thieves, andknaves, and the conductor of the souls of the dead to the infernal regions. ByPenelope, Pan. By the Greeks he was calledHermes.By Mnemos´y-ne.The Nine Muses.TETHYSWife ofOceanus; for offspring, seeOceanusCli´opresided over History.-SeeDictionary of Mythology.Calli´o-pepresided over eloquence and epic poetry.Er´atopresided over lyric and amorous poetry.Thali´apresided over pastoral and comic poetry and festivals.Melpom´e-nepresided over tragedy.Terpsich´o-represided over dancing.Euter´pepresided over music.Polyhym´niapresided over singing and rhetoric.Ura´niapresided over astronomy.THEAWife ofHyperion; the mother of rivers, and of about three thousand daughters, calledOcean´i-des.By Euryn´o-me.Graces.Agla´ia-Three beautiful virgins, attendants on Venus; presided over kindness and good offices, and were supposed to give to beauty its charms; represented dancing in a circle with their hands joined.Thali´aEuphros´y-neCŒLUS or URANUS,i.e.Heaven, andTERRAor TITÆA,i.e.Earth.-hadSATURNorCronos,god of Time, had byRheasame asOps, same asCybele.By Sem´e-le.Bacchus, god ofwine; by his wifeAriadne, Thoas, Œnopion, Ceranus, Tauropolis, and others.By Metis.Minerva, the goddess ofwisdom,war, and theliberal and useful arts.By Dione.Venus, said to have been borne in the foam of the sea; the goddess ofloveandbeauty, and mistress of the graces; wife ofVulcan; for offspring, seeVulcan.MNEMOSYNEMother of the nineMuses.By Ceres.Pros´erpine, wife of Pluto,queenof hell, presided over death. She was stolen away by Pluto while gathering flowers in Sicily, and became the mother of theFatesandFuries, which see underDictionary.By Euro´pa.Minos,Rhadamanthus, andÆ´acus, three inflexible judges of Hades.THEMISMother of Astræa, goddess of Justice.By Leda.-SeeDictionary of Mythology.CastorandPollux.By Dan´a-e.Per´seus.By Anti´o-pe.Amphi´onandZethus.CYBELEOPS or RHEA, wife ofSaturn; the goddess ofall things; styledMagna MaterorGreat Mother,Bona MaterorGood Mother; for off-spring, seeSaturn.By Segesta.Æolus, whose offspring were the various Winds.By Alcmena.Hercules, whose descendants were the Heraclidæ.VESTA, the goddess offire, and patroness ofVestal Virgins, who had the care of the sacred fire in the temple of Vesta at Rome, which was kept continually burning.CERES, the goddess ofcornandharvest. The famousEleusinian mysterieswere celebrated in honor of Ceres, during the representation of which it was death to speak; as it was also to reveal afterwards what took place.LATONIA, celebrated for her beauty, and for being greatly beloved by Jupiter and persecuted by Juno.NEPTUNE, the god of thesea, the father of rivers and fountains, and, next to Jupiter, the most powerful deity; had byAmphitrite, TRITON, his father’s companion and herald.OCEANUSThe god of water, to whom the ancients recommended themselves when going on a voyage, had by Tethys.PLUTO, the god of theinfernal regions, ofdeathandfunerals; the dogCer´berus, a frightful mastiff with three heads, and a tail like a serpent, watches at his feet, and threeHar´pies, winged monsters, hover about him.-AMPHITRITE had byNeptuneTRITON, who had no offspring.CYLMENE had byJapetusATLAS, also Menœtius, Prometheus, Epimetheus, and others.PHORCYS had byCeto-The Gorgons, viz., Medusa, Stheno, and Euryale; three sisters whose heads were covered with vipers.The Graiæ, viz., Pephredo, Enyo, and Dinon.ACHELOUS had byCalliope.TheSirenswere three sea nymphs, namedParthen´ope,Lige´ia, andLeuco´sia, having the form of a woman above the waist, and the rest of the body like a flying fish.The Harpies, viz., Aello, Ocypete, and Celæus.HYPERION, god of the Sun, had byThea, AURORA, the goddess of themorning; represented riding in a rose-colored chariot drawn by white horses, usually covered with a veil, the morning star appearing overhead. She was calledrosy-fingered, because she scattered roses; byTithon´us, a mortal, she had Memnon and Æmathion.JAPETUS, father of mankind, had byClymene, ATLAS, also Prometheus, Epimetheus, Menœtius, and others, calledJapitonides.EREBUS and NOX-had-Light, or Day, Somnus, Mors, and Charon, the Ferryman-NoxorNight,MorsorDeath,SomnusorSleep, andMorpheus(the minister of Somnus, who brought dreams to men) were infernal divinities.Momus, god of laughter and satire, son of Somnus and Nox.Ancient Roman Sun-god—Janus, the god of theyear, presided over the gates of heaven, and over peace and war; represented with two faces. His temple in Rome was open in time of war and shut in time of peace.
CHAOSProduced EREBUS, god ofdarkness, NOX, goddess ofnight, and TERRA,Earth.TERRA or TITÆAproducedCŒLUSor URANUS,Heaven.CŒLUS or URANUS,i.e.Heaven, andTERRAor TITÆA, i.e.Earth. hadTITANOldestof the twelve Titans.THE CYCLOPSGiants,at first three in number:Arges,Brontes,Steropes.BRIAREUSAfamous giant called by men Ægæon, and by the gods Braireus.TETHYSWifeofOceanus; for offspring, seeOceanus.THEAWifeofHyperion; the mother of rivers, and of about three thousand daughters, calledOcean´i-des.SATURNorCronos,god of Time, had byRheasame asOps, same asCybele.JUNO, wife and sister of Jupiter, queen of the gods, and of Heaven and Earth.JUPITERorZeus, the most powerful of all the gods; king of gods and men, hadBy Them´is.Astræa, the goddess ofjustice;Nemesis, ofvengeance.By Juno.Mars, the god ofwar; byVenus, Anteros, Harmonia; the goddess ofyouth; once cupbearer to Jupiter.Hebe, by her husbandHercules, Alexiares and Anicetus.Typhon, by the monsterEchidna, Chimæra and Sphinx.Vulcan, the god offireand ofblacksmiths, and husband of Venus; by his wifeVenus, Cupid; byMedusa, Cacus, byJuno, Cæculus.By Lato´na.Apollo, the god ofpoetry,music,eloquence,medicine,the fine arts,augury, andarchery.Diana, the goddess ofhunting, the patroness of chastity, presided also over childbirth.By Ma´ia.Mercury, themessengerof the gods, the god ofeloquenceandcommerce, the patron oftravellers,thieves, andknaves, and the conductor of the souls of the dead to the infernal regions. ByPenelope, Pan. By the Greeks he was calledHermes.By Mnemos´y-ne.The Nine Muses.Cli´opresided over History.Calli´o-pepresided over eloquence and epic poetry. (SeeDictionary of Mythology.)Er´atopresided over lyric and amorous poetry. (SeeDictionary of Mythology.)Thali´apresided over pastoral and comic poetry and festivals. (SeeDictionary of Mythology.)Melpom´e-nepresided over tragedy. (SeeDictionary of Mythology.)Terpsich´o-represided over dancing. (SeeDictionary of Mythology.)Euter´pepresided over music. (SeeDictionary of Mythology.)Polyhym´niapresided over singing and rhetoric. (SeeDictionary of Mythology.)Ura´niapresided over astronomy. (SeeDictionary of Mythology.)By Euryn´o-me.Graces.(Three beautiful virgins, attendants on Venus; presided over kindness and good offices, and were supposed to give to beauty its charms; represented dancing in a circle with their hands joined.)Agla´iaThali´aEuphros´y-neBy Sem´e-le.Bacchus, god ofwine; by his wifeAriadne, Thoas, Œnopion, Ceranus, Tauropolis, and others.By Metis.Minerva, the goddess ofwisdom,war, and theliberal and useful arts.By Dione.Venus, said to have been borne in the foam of the sea; the goddess ofloveandbeauty, and mistress of the graces; wife ofVulcan; for offspring, seeVulcan.By Ceres.Pros´erpine, wife of Pluto,queenof hell, presided over death. She was stolen away by Pluto while gathering flowers in Sicily, and became the mother of theFatesandFuries, which see underDictionary.By Euro´pa.Minos,Rhadamanthus, andÆ´acus, three inflexible judges of Hades.By Leda.CastorandPollux. (SeeDictionary of Mythology.)By Dan´a-e.Per´seus.(SeeDictionary of Mythology.)By Anti´o-pe.Amphi´onandZethus. (SeeDictionary of Mythology.)By Segesta.Æolus, whose offspring were the various Winds.By Alcmena.Hercules, whose descendants were the Heraclidæ.VESTA, the goddess offire, and patroness ofVestal Virgins, who had the care of the sacred fire in the temple of Vesta at Rome, which was kept continually burning.CERES, the goddess ofcornandharvest. The famousEleusinian mysterieswere celebrated in honor of Ceres, during the representation of which it was death to speak; as it was also to reveal afterwards what took place.LATONIA, celebrated for her beauty, and for being greatly beloved by Jupiter and persecuted by Juno.NEPTUNE, the god of thesea, the father of rivers and fountains, and, next to Jupiter, the most powerful deity; had byAmphitrite, TRITON, his father’s companion and herald.PLUTO, the god of theinfernal regions, ofdeathandfunerals; the dogCer´berus, a frightful mastiff with three heads, and a tail like a serpent, watches at his feet, and threeHar´pies, winged monsters, hover about him.MNEMOSYNEMotherof the nineMuses.THEMISMotherof Astræa, goddess of Justice.CYBELEOPSor RHEA, wife ofSaturn; the goddess ofall things; styledMagna MaterorGreat Mother,Bona MaterorGood Mother; for off-spring, seeSaturn.OCEANUSThegod of water, to whom the ancients recommended themselves when going on a voyage, had by Tethys.AMPHITRITE had byNeptuneTRITON, who had no offspring.CYLMENE had byJapetusATLAS, also Menœtius, Prometheus, Epimetheus, and others.PHORCYS had byCeto{The Gorgons, viz., Medusa, Stheno, and Euryale; three sisters whose heads were covered with vipers. {The Graiæ, viz., Pephredo, Enyo, and Dinon.ACHELOUS had byCalliope. TheSirenswere three sea nymphs, namedParthen´ope,Lige´ia, andLeuco´sia, having the form of a woman above the waist, and the rest of the body like a flying fish.The Harpies, viz., Aello, Ocypete, and Celæus.HYPERION, god of the Sun, had byThea, AURORA, the goddess of themorning; represented riding in a rose-colored chariot drawn by white horses, usually covered with a veil, the morning star appearing overhead. She was calledrosy-fingered, because she scattered roses; byTithon´us, a mortal, she had Memnon and Æmathion.JAPETUS, father of mankind, had byClymene, ATLAS, also Prometheus, Epimetheus, Menœtius, and others, calledJapitonides.EREBUS and NOX had Light, or Day, Somnus, Mors, and Charon, the FerrymanNoxorNight,MorsorDeath,SomnusorSleep, andMorpheus(the minister of Somnus, who brought dreams to men) were infernal divinities.Momus, god of laughter and satire, son of Somnus and Nox.Ancient Roman Sun-god—Janus, the god of theyear, presided over the gates of heaven, and over peace and war; represented with two faces. His temple in Rome was open in time of war and shut in time of peace.
SCREENS OF LIGHT CAST BY INVISIBLE ATOMS
IMMENSELY ENLARGED REPRESENTATIONS OF ATOMS(1) of Ordinary Matter; (2) of Radium
IMMENSELY ENLARGED REPRESENTATIONS OF ATOMS
(1) of Ordinary Matter; (2) of Radium
Here is seen an invisible speck of radium throwing out invisible atoms that sparkle into sight on a film. This stream of atoms will pour forth for 2500 years before the radium ceases to exist, thus showing the marvelous energy stored up in the smallest particle. These flying particles fall on the screen or film like hailstones splashing on the surface of water, and the splash is visible, while the radium itself and flying atoms are not. This is the nearest men have yet come to seeing an actual atom.
Here is seen an invisible speck of radium throwing out invisible atoms that sparkle into sight on a film. This stream of atoms will pour forth for 2500 years before the radium ceases to exist, thus showing the marvelous energy stored up in the smallest particle. These flying particles fall on the screen or film like hailstones splashing on the surface of water, and the splash is visible, while the radium itself and flying atoms are not. This is the nearest men have yet come to seeing an actual atom.
Large photograph(268 kB)
HISTORICAL DEVELOPMENT OF THE SCIENCES
OUTLINES OF SCIENCE FOR SCHOOLS
PRACTICAL MATHEMATICS FOR DAILY USE:Business and Industrial Arithmetic, Everyday Applications of Percentage, Weights and Measures, Mensuration and its Applications
COMMERCIALAND INDUSTRIAL LAW
PHYSICS: ITS PRINCIPLES AND APPLICATIONS
CHEMISTRY: ITS THEORY AND USES
THE CHEMISTRY OF COMMON THINGS
REVISED TABLE OF CHEMICAL ELEMENTS
GREAT INVENTIONS AND SCIENTIFIC DISCOVERIES
RELATION OF THE GOVERNMENT TO SCIENCE
BOOK OF SCIENCE AND INVENTION
Science in its widest significance is sometimes defined as the correlation of all knowledge. In this sense it would includephilosophy. In a more restricted and generally accepted sense, the term is applied to thesystematizeddivisions of knowledge.
Science and philosophyresembleeach other in so far as they both have to do with knowledge; but while the latter deals with the whole sum of knowledge and goes back to generalized first principles, the former takes up special branches of it. That is, a science is such in fact when a sufficient number of interrelated facts are so arranged and classified by referring them to the general truths and principles on which they are founded that they constitute a well-certified and more or less complete branch of knowledge.
From the present development of knowledge the separate entities of the universe are five—namely, ether, matter, energy, life, and mind. The first three are inseparable agents in the simplest phenomena that occur in nature. They may ultimately be reduced to two, or, conceivably, to one. It is with these that the various branches of science have to deal—to observe, to experiment, to classify, to define.
Classification of the Sciences.—The sciences may be grouped in two ways.First, from what has been said above, they may be divided into:
(a) thephysicalsciences, which have to do with inorganic nature—that is with the laws and properties of matter, energy, and ether;
(b) thebiologicalsciences, which consider the laws of life; and
(c) thepsychicalsciences, which deal with the phenomena of mind.
Second.—Another, and probably more practical, division is that of (a)pureortheoreticsciences, and (b)appliedorpracticalsciences. The latter consist of those branches which deal with facts, events, or phenomena as explained, accounted for, or produced by means of powers, causes, or laws; the former as the knowledge of these powers, causes, or laws, considered apart or as pure from all applications. To the class of pure or fundamental sciences belong mathematics, physics, chemistry, psychology, and sociology; to the applied or concrete belong geology, mineralogy, botany, zoology, meteorology, geography, ethics, politics, law, jurisprudence, logic, grammar, rhetoric, philology, and political economy; navigation, engineering, and practical mechanics; surgery, medicine, materia medica, etc.
Methods of Science.—The great method of scientific inquiry is experiment—the laboratory. Contrasted withexperimentisobservation. But even in astronomy, emphatically an observational science, experiment plays an important part. The dynamical knowledge which Newton developed into the cosmic law of gravitation was founded on experiment. Meteorology, again, has made great strides in these days by appealing to laboratory experiments for elucidation of its phenomena. Likewise in biology, botany, and zoology experiment has led to striking discoveries; while such branches as embryology and bacteriology are as truly experimental as chemistry itself.
In the psychical group of sciences the method of experimenting still awaits development. The complexity of the problems presented, and the manner in which they affect the welfare and happiness of humanity, render social and political experimenting excessively hazardous. Such sciences as those studied by the economist, the ethnologist, the moralist, or the theologian are of necessity essentially observational.
It would be difficult to overestimate the extent to which mathematics enters into the conditions of everyday life. In its elementary stages, as the science of number, it teaches us the relations of magnitude, and enables us to build up a system of calculation and measurement which, applied to the relations observed to exist in nature, gives results of far-reaching importance.
The properties of number are investigated in arithmetic, and methods examined by which those engaged in practical science are able to work out their results to any degree of approximation.
With the help of algebra, we arrive at a system of logarithms by which many of these results may be reached with the minimum of labor.
The measurement of lines and angles, by methods investigated in geometry and trigonometry, enables us to calculate areas, and work out various problems met with in surveying, and is of the first importance in astronomy.
Arithmetic, which deals with the properties of numbers, forms the basis of all mathematical calculation. (For theprimarytreatment of numbers, see underThe Child World.)
A Fraction is one or more of the equal parts into which a unit has been divided. ACommon Fractionis expressed by two numbers; the one written above the line is called the Numerator, the one below, the Denominator: both, called the Terms, denote the value of the fraction.
Thus, in the fraction3⁄4, the denominator 4, denotes that a unit or whole thing has been divided into four equal parts; and the numerator 3, shows that three of those parts are taken or expressed in the fraction.
AProper Fractionis one whose numerator is less than its denominator; as1⁄2,3⁄4,7⁄8, etc. Its value is always less than 1.
AnImproper Fractionis one whose numerator is equal to, or greater than its denominator, as5⁄5,9⁄7,30⁄12, etc. Its value is never less than 1.
AMixed Numberis a whole number and a fraction; as 32⁄5, 101⁄2, 62⁄3.
The mixed number means that there are whole things taken together with a fraction of another.
AComplex Fractionis one in which the numerator or denominator, or both, are fractions.
Thus31⁄723⁄8,15⁄6×3⁄4,15⁄178, are complex fractions.
A very good method of learning the combinations in small fractions is by the use of paper or cardboard disks.
Cut out a large number of them, and, in order to avoid trouble later on, it might be better to have the disks all of one size—about 4 inches in diameter.
Explanation:—Take a circular disk and cut it into two equal parts. Then proceed in this manner: What is this part called? What is other part called? How many halves in the whole circle? One-half and one-half are what? One-half taken away from one leaves what? If I take a half two times, what do I get? How many halves in a whole?
Now I will write these—
12+12=
1 ÷ 2 =
1 less12=
1 -12=
2 ×12=
1 divided by12=
Give me the answers and I will write them.
Drawings showing the “placing” of disks for number combinations can then be made; as,