Books Books 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. The philosophical and mathematical commentaries of Proclus ... on the first ... - Page 11 ## The Usefulness of Mathematical Learning Explained and Demonstrated: Being ...

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... ## Elements of Geometry: With Their Application to the Mensuration of ...

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... ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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... ## The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

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... ## The First Six Books: Together with the Eleventh and Twelfth

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.... ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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... ## Elements of Geometry: Containing the First Six Books of Euclid, with Two ...

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... ## The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

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.... ## Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

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,... 