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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. "
The philosophical and mathematical commentaries of Proclus ... on the first ... - Page 11
by Proclus (Diadochus.) - 1789
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...described from any centre, at any distance from that centre. AXIOMS. I. THINGS which are equal to the same 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. If equals be added to unequals, the wholes are unequal....
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...from any centre, at any distance from that centre. AX IOM S. I. THINGS which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. ill. If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...described from any centre, at any distance from that centre. AXIOMS. I. THINGS which are equal to the same 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...from any centre, at any distance from that centre. AXIOMS. I. 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 equate be taken from equals, the remainders are equal. IV. If equals be added to uaequals, the wholes...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...distance from that centre. AXIOMS. I. THINGS which are equal to the same are equal to one another. 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...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 pages
...proposition. An Axiom is a self-evident truth. I AXIOMS. I. — 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. IV.— If equals be added to unequals, the wholes are...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...from that eentre. AXIOMS, I. THlNGS whieh are equal to the same thing are equal to one another, n. If equals be added to equals, the wholes are equal. III. If equals be taken from equal?, the remainders are equal. IV. If equals be added to unequals, the wholes are...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...any centre at any distance from that centre. AXIOMS. I. * 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. IV. If equals be added to unequals, the wholes are...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 333 pages
...from any centre, at any distance from that centre. Axioms. iTHINGS 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.' IV. If equals be added to unequals, the wholes are...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...described from any centre, at any distance from that centre. AXIOMS. I. THINGS which are equal to the same 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...
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