 | John Playfair - 1844 - 338 σελίδες
...but two to the last but one of the second rank ; and as the third is to the fourth of the first'rank, so is 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,... | |
 | Euclides - 1845 - 546 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...definition. It is demonstrated in Prop. 23, Book v. AXIOMS. I. EQUIMULTIPLES of the same, or of equal magnitudes, are equal to one another. II. Those magnitudes,... | |
 | Euclid - 1845 - 218 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 23rd Prop, of Book 5. AXIOMS. I. Equimultiples of the same, or of equal magnitudes, are equal to... | |
 | Euclid, John Playfair - 1846 - 334 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,... | |
 | Euclides - 1846 - 292 σελίδες
...last but one of the second rank ; and the third to the fourth of the first rank, as the last but three to the last but two of the second rank ; and so on in a cross order ; and the inference is made as before (a. 23). AXIOMS. i. Equimultiples of the same, or of equal magnitudes, are equal to... | |
 | Euclides - 1848 - 52 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 18th definition. It is demonstrated in Prop. 23, Bookv. AXIOMS. I. EQUIMULTIPLES of the same, or of equal magnitudes, are equal to one another. II.... | |
 | Euclides - 1853 - 176 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, so is the third from the hist to the last but two of the second rank, and so on in a cross order : and the inference is as in... | |
 | Royal Military Academy, Woolwich - 1853 - 400 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, sois the third from the last to the last but two of the second rank ; and so on in a cross order ;... | |
 | Euclides - 1855 - 270 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...definition. It is demonstrated in Prop. 23, Book V. [The Latin terms explained in these eight definitions are usually roplaced by the English words which... | |
 | Euclides - 1855 - 230 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 19th definition. It is demonstrated in Proposition XXIII., book 5. The following table will serve to... | |
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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... 
