The Propositions of the Fifth Book of Euclid Proved Algebraically: with an Introduction, Notes, and QuestionsJohn Henry and James Parker, 1862 - 79 sider |
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Side 30
... excess of the first above the second is to the second , as the excess of the third above the fourth is to the fourth . Prop . XVII . c If a bed , " dividendo " a - b : b :: cd : d ; or , which is the same thing ( vide Prop . XVII ...
... excess of the first above the second is to the second , as the excess of the third above the fourth is to the fourth . Prop . XVII . c If a bed , " dividendo " a - b : b :: cd : d ; or , which is the same thing ( vide Prop . XVII ...
Side 31
... excess above the second , as the third to its excess above the fourth . Prop . E. If a : b :: c : d , “ convertendo ” a : a XVIII . - b :: c ―d . Ex æquali ( sc . distantiâ ) , or ex æquo , from equality of distance : when there is any ...
... excess above the second , as the third to its excess above the fourth . Prop . E. If a : b :: c : d , “ convertendo ” a : a XVIII . - b :: c ―d . Ex æquali ( sc . distantiâ ) , or ex æquo , from equality of distance : when there is any ...
Side 53
... excess of the first above the second is to the second as the excess of the third above the fourth is to the fourth . " This is substantially the same proposition as that enuntiated and proved in the text ; for if a + b , b , c + d , and ...
... excess of the first above the second is to the second as the excess of the third above the fourth is to the fourth . " This is substantially the same proposition as that enuntiated and proved in the text ; for if a + b , b , c + d , and ...
Side 56
... excess above the second , as the third to its excess above the fourth . a , b , c , d . Let a b :: c : d . Then shall a : a - b :: c : c - d . Because a : b :: c : d , therefore , dividendo , a - b : b :: c - d : d ; therefore ...
... excess above the second , as the third to its excess above the fourth . a , b , c , d . Let a b :: c : d . Then shall a : a - b :: c : c - d . Because a : b :: c : d , therefore , dividendo , a - b : b :: c - d : d ; therefore ...
Side 63
... excess of the first and fifth shall be to the second as the excess of the third and sixth to the fourth . α Because C e and = b d - b b a therefore whence α -e b = f b d = = C d d - as before ; f . d ; and therefore a - e : b :: c - f ...
... excess of the first and fifth shall be to the second as the excess of the third and sixth to the fourth . α Because C e and = b d - b b a therefore whence α -e b = f b d = = C d d - as before ; f . d ; and therefore a - e : b :: c - f ...
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The Propositions of the Fifth Book of Euclid Proved Algebraically George Sturton Ward Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
&c.-Q. E. D. PROPOSITION a b c d ÆSCHYLUS alternando Aristophanes Aristotle arithmetic b a greater ratio b+d+f BOOK OF EUCLID braically c=md CHARLES CAVENDISH CLIFFORD cloth componendo compound ratio compounded of ratios CORNELIUS NEPOS dividendo duplicate ratio Edition equimultiples Euclid EUMENIDES Euripides Ex æquali expressed algebraically Fcap FIFTH BOOK fifth definition four magnitudes G to H geometrical GEORGE MOBERLY GEORGICS Grammar greater than nd greater than unity Greek and Latin Greek Plays inferred invertendo last ratios LECTURES length less magnitude taken magnitudes be proportionals manner MOUNTAGUE BERNARD multiple nitudes Notes separate number of magnitudes OXFORD POCKET CLASSICS PHILOCTETES Prop property of numbers proportionals when taken quantities ratio compounded remaining ratio Rolls of Parliament sewed shewn Text and Notes third THOMAS GAISFORD Thucydides tiples triplicate ratio University of Oxford vols volume whence wherefore whole number
Populære avsnitt
Side 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...
Side 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,
Side 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
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.