 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...second is to the third of the first rank, so is the last but two to the last but one of the second rank ; and as the third is to the fourth of the first...in a cross order : and the inference is as in the eighteenth definition. It is demonstrated in the twentythird proposition of Book V. Thus if there be... | |
 | Euclid, Robert Simson - 1829 - 548 σελίδες
...second is to the third of the first rank, so is the last but two to the last but one of the second.rank; and as the third is to the fourth of the first rank,...is as in the 18th definition. It is demonstrated in the 2 3d Prop. of book 5. AXIOM8. I. EQUIMDLTIPLES of the same, or of equal magnitudes, are equal to... | |
 | John Playfair - 1833 - 346 σελίδες
...to the last but one of the second rank ; and as the third is to the fourth of the first rank, so isr the third from the last, to the last but two, of the second rank ; and so on in a cross, or inverse, order ; and the inference is as in the 19th definition. It is demonstrated in the 23d Prop,... | |
 | Euclid - 1835 - 540 σελίδες
...second is to the third of the first rank ; so is the last but two to the last but one of the second rank, and as the third is to the fourth of the first...is as in the 18th definition. It is demonstrated in the 23d Prop, of Book 5. AXIOMS. I. EQUIMULTIPLES of the same, or of equal magnitudes, are equal to... | |
 | 1836 - 488 σελίδες
...of the first rank, so is the last but two to the last but one of the second rank ; and as the third to the fourth of the first rank, so is the third from...last to the last but two, of the second rank ; and so in a cross, or inverse, order ; and the inference is as in the 19th definition. AXIOMS. 1. Equimultiples... | |
 | John Playfair - 1837 - 332 σελίδες
...second is to the third of the first rank, so is the last but two to the last but one of the second rank ; and as the third is to the fourth of the first...but two, of the second rank ; and so on in a cross, or inverse, order ; and the inference is as in the 19th definition. It is demonstrated in the 23d Prop,... | |
 | Andrew Bell - 1837 - 290 σελίδες
...second is to the third of the first rank, so is the last but two to the last but one of the second rank ; and as the third is to the fourth of the first...the last but two of the second rank ; and so on in an indirect order. The following are some additional algebraical expressions which are convenient for... | |
 | Euclides - 1841 - 378 σελίδες
...second is to the third of the first rank, so is the last but two to the last but one of the second rank; and as the third is to the fourth of the first...on in a cross order: and the inference is as in the 1Sth definition. It is demonstrated in Prop. 23rd. of Book 5. AXIOMS. L EQUIMULTIPLES of the same,... | |
 | Oliver Byrne - 1841 - 144 σελίδες
...second is to the third of the first rank, so is the last but two to the last but one of the second rank; and as the third is to the fourth of the first...and so on in a cross order : and the inference is in the 18th definition. It is demonstrated in 23 Prop., Book v. Thus, if there be two ranks of magnitudes,... | |
 | John Playfair - 1842 - 332 σελίδες
...second is to the third of the first rank, so is the last but two to the last but one of the second rank ; and as the third is to the fourth of the first...but two, of the second rank ; and so on in a cross, or inverse, order; and the inference is as in the 19th definition. It is demonstrated in the 23d Prop,... | |
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This term is used when the first magnitude is to the second of the first rank, as the last but one is to the last of the second rank; and as the second is to the third of the first rank, so is the last but two to the last but one of the second rank; and... 
