 | Isaac Barrow - Mathematics - 1734 - 616 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 - 296 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 - 488 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 - 534 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 - 552 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 - 534 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... | |
 | Euclid, John Playfair - Euclid's Elements - 1795 - 462 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 - 374 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 - Circle-squaring - 1804 - 468 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 - 530 pages
...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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THINGS which are equal to the same 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. 
