The Propositions of the Fifth Book of Euclid Proved Algebraically: with an Introduction, Notes, and Questions
John Henry and James Parker, 1862 - Geometry, Algebraic - 79 pages
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The Propositions of the Fifth Book of Euclid Proved Algebraically
George Sturton Ward
No preview available - 2016
Common terms and phrases
&c.-Q. E. D. PROPOSITION a b c d algebraical arithmetic Author b a greater ratio CLASSICS cloth College compounded of ratios contain continual corresponding definition delivered Edition English equal equimultiples Ex æquali exact excess expressed Fcap former four magnitudes fourth fractions G to H geometrical Grammar Greek and Latin HISTORY includes inferred Introduction invertendo kind LECTURES length less lines LOGIC magnitude taken manner multiple Notes separate number of magnitudes Oxford pair Persius Plays portionals pounded Professor proof Prop proportionals PROPOSITION proved quantities rank ratio compounded relation represent Schools sewed shewn Shilling SHORT side sixth square symbols taken Text and Notes third Translated triplicate unity University Vide vols volume whence wherefore whole
Page 12 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 62 - If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes, the same ratio which the first of the others has to the last. NB This is usually cited by the words "ex sequali,
Page 58 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words
Page 54 - Ij the first be to the second as the third to the fourth, and if the first be a multiple, or a part of the second ; the third is the same multiple, or the same part of the fourth.
Page 38 - IF one magnitude be the same multiple of another, which a magnitude taken from the first is of a magnitude taken from the other ; the remainder shall be the same multiple of the remainder, that the whole is of the whole.
Page 25 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.
Page 57 - IF there be three magnitudes, and other three, which, taken two and two, have the same ratio ; if the first be greater than the third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less...
Page 31 - ... that they are proportionals when taken two and two of each rank, and it is inferred, that the first is to the last of the first rank of magnitudes, as the first is to the last of the others: ' Of this there are the two follow' ing kinds, which arise from the different order in ' which the magnitudes are taken two and two.