The Educational Significance of Sixteenth Century Arithmetic from the Point of View of the Present Time (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 Excerpt: ...proportio. que. nihil aliud eft: q earum inter fe comparatio eiufdem quoqj generis quantitates effe debent: inter quas cadit proportio. Veluti duo numeri, duae lineae, due fuperficies, duo corpora duo loca, duo tempora. neqs enim linea maior aut minor fuperficie eft, aut corpora: nec tempus loco maius eft, aut minus, fed linea linea: fuperficies fuperficie: corpus.corpore. fola enim, quae unius funt generis: inter fe comparabilia funt." Fol. ij verso. "Quippe proportio apud ueteres in tria fecatur genera, quorum unum eft difcretorum, uidelicet numerorum: quod uocant Arithmeticum. Alterum eontinuorum: quod geometricutn appellant. Tertium fonorum et concentuum' quod armonicfi nuncupant, ex illoru utroaj mixtu: qj mufica in paufis et prolationibus tepus fpectet: in uihrante nocu notarumqj diuifione, numeros." Fol. i, verso. "Vnde fit: ut qucumqj proportio occurrit in numeris: eadem reperiatur in omni genere eontinuorum. puta in lineis, fuperficiebus, corporibus, et temporibus." Fol. i2 recto. among themselves. Quantities which form a proportion must be of the same kind, as two numbers, two lines, two surfaces, two solids, two like orders, and not, a line is greater than a surface, or solid, or time is greater or less than a space, but line is comparable with line, surface with surface, solid with solid, and so on. "Among the ancients proportion is divided into three classes, arithmetic, geometric and harmonic. "Just as proportion occurs in numbers, so it is found in all continua, as in lines, surfaces, solids, and time." Kinds of Rational Proportion 1 "Any quantity compared with another is equal or unequal to it. A quantity is equal to another when it does not exceed that quantity, or is not exceeded by it, as a cu...