| Isaac Barrow - Mathematics - 1734 - 612 pages
...dpolloniits has illuitrated that which Ramus calls the moft bright Sun in the Mathematics, That thofe **Things, which are equal to the fame, are equal to one another,** by a Demonftration fetched from hence. Let the two Magnitudes A and C be each fingularly fuppofed equal... | |
| Thomas Simpson - Geometry - 1760 - 300 pages
...magnitudes, unto ratios, ** viz. that a magnitude cannot be both greater " and lefs than another. That thofe **things which " are equal to the fame are equal to one another,** " is a moft evident Axiom when uriderftood o| " magnitudes, yet Euclid does not make ufe of it " to... | |
| Robert Simson - Trigonometry - 1762 - 466 pages
...m. And that a circle may be defcribed from any center, at any diftance from that center. AXIOMS. I **THINGS which are equal to the fame are equal to one...If equals be added to equals, the wholes are equal.** m. If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the... | |
| Robert Simson - Trigonometry - 1775 - 520 pages
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB; but **things which are equal to the fame are equal to one another** d ; therefore CA is equal to CB ; wherefore CA, AB, BC are equal to one another; and the triangle ABC... | |
| Euclid - 1781 - 550 pages
...a circle may be defcribed from any centre, at any <Ji fiance from that centre. AXIOMS. '•'• I. **THINGS which are equal to the fame are equal to one...added to equals, the wholes are equal. III. If equals** be taken from equals, the remainders are equaL IV. If equals be added to unequals, the wholes are unequal.... | |
| Robert Simson - Trigonometry - 1781 - 466 pages
...has been proved that CA is equal to finition. AB; therefore CA, CB are each of them equal to AB. but **things which are equal to the fame are equal to one another** d; therefore d. id AxiCA is equal to CB. wherefore CA, AB, BC are equal to one ano- cm. ther. and the... | |
| John Playfair - Trigonometry - 1795 - 444 pages
...from any centre, at any diftance from that centre. AXIOMS, v THINGS which are equal to the fume thing **are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals** be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are... | |
| Alexander Ingram - Trigonometry - 1799 - 351 pages
...And that a circle may be dei'cribed from any centre, at any diftance from that centre. ' AXIOMS. I. **THINGS which are equal to the fame, are equal to one...added to equals, the wholes are equal. III. If equals** be taken from equals, the remainders are equal. If equals be added to unequals, the wholes are unequal.... | |
| John Playfair - Euclid's Elements - 1804 - 470 pages
...any diftance from that centre. . AXIOMS. I. HT1 HINGS which are equal to the fame thing are equal JL **to one another. II. If equals be added to equals, the wholes are equal.** Til. If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals,... | |
| Robert Simson - Trigonometry - 1804
...BA. but it has been proved that CA is equal to AB; therefore CA, CB are each of them equal to AB. but **things which are equal to the fame are equal to one another** d; therefore d. CA is equal to CB. wherefore CA, AB, BC are equal to one another, and the triangle... | |
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