 | Rev. John Allen - 1822 - 516 pages
...of all in the other (12. 5 -E«.), and so is the former figure to the other, the former figure being to the former sum, and the latter figure to the latter sum, in the ratio of equality (by Lemma 3). Cor. Hence if two quantities of any kind, be any how divided into... | |
 | Isaac Newton, George Leigh Cooke - 1850 - 176 pages
...parallelograms in one are severally Fig. 4. sum of all in the other; and so is one figure to the other ; because (by Lemma III.) the former figure is to the former sum, and the latter figure to the paral- « lelograms in the other ; so, by composition, is the sum of all in . ~-~^ \ \ A d to the latter... | |
 | Benjamin Theophilus Moore - 1863 - 320 pages
...be the same, each to each; then, the two figures AacE, PprT are to one another in that same ratio. For, as the parallelograms are each to each, so, componendo,...figure to the latter sum in a ratio of equality. The following proof will assist the student in understanding this important Lemma. Let A*, AS, A, ...,«,,... | |
 | Sir Isaac Newton - 1863 - 316 pages
...AacE, PprT are ultimately in the same ratio, and so the figures AacE, PprT are in that same ratio ; for, by Lemma III, the former figure is to the former...figure to the latter sum in a ratio of equality.] QED Cor. Hence, if two quantities of any kind whatever, be divided into any, the same, number of parts;... | |
 | Albert Taylor Bledsoe - 1886 - 253 pages
...of all in the other, and so the one figure to the other ; because (by Lemma III.) the former figure to the former sum, and the latter figure to the latter sum, are both in the ratio of equality. QED" Now this demonstration, it will be perceived, proceeds on the... | |
 | Isaac Newton - 1900 - 320 pages
...ultimately in the same ratio, and so the figures AacE, PprT are in that same ratio ; for, by Lemma 1IL, the former figure is to the former sum and the latter...figure to the latter sum in a ratio of equality.] QED COR. Hence, if two quantities of any kind whatever be divided into any, the same, number of parts,... | |
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For as the parallelograms in the one are severally to the parallelograms in the other, so (by composition) is the sum of all in the one to the sum of all in the other; and so is the one figure to the other; because (by Lem. Ill) the former figure to the... 