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" If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. "
The philosophical and mathematical commentaries of Proclus ... on the first ... - Page 12
by Proclus (Diadochus.) - 1789
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...remainders are equal. IV. If equals be added to unequals, the wholes are unequal V. If equals betaken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are halves of the same, are equal to one another....
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...the wholes are equal. HI. If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are unequal. V. If equals...unequals, the remainders are unequal VI. Things which are doubles of the same thing, are equal to one another. VII. Things which are halves of the same thing,...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...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. V. —...the remainders are unequal. VI. — Things which are doubles of the same thing, are equal to one another. VII. — Things which are halves of the same thing,...
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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
...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 unequal. V. If equals...from unequals, the remainders are unequal. VI. Things whieh are doubles of the same thing, are equal to one another, VII. Things whieh are halves of the...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...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. V. If equals...remainders are unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are halves of the same, are equal to one another....
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...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. V. If equals be taken from unequals, the remainders arc unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...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. V. If equals...remainders are unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are halves of the same, are equal to one another....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...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. V. If equals be taken from unequals, the remainders arc unequal VI. 'Things which are doubles of the same thing, are equal to -Book*!, one another. \~~Y^~'...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...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. V. If equals be taken from unequals, the remainders arc unequal. . VI. Things which are doubles of the same are equal to one another. VII. Things which...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...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. V. If equals...remainders are unequal. VI. Things which are double of the same, are equal to one another. vn. Things which are halves of the same, are equal to one another....
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