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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 geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...the wholes are equal. Ш. 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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Mensuration of Lines, Areas, Surfaces, and Volumes ...

Robert Rawson - 1856 - 178 pages
...the wholes are equal. m. 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, VL Things which are double of the same, are equal to one another. vn. Things which are halves of the...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...remainders are equal. IV. When equals are added to unequals, the wholes are unequal. V. When equals are taken from unequals, the remainders are unequal. VI. Things which are double of the same or equal things, are equal. VII. Things which are halves of the same thing, are equal. VIII. Every...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...wholes are equal. m. , 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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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 472 pages
...remainders are equal. IV. When equals are added to unequals, the wholes are unequal. V. When equals are taken from unequals, the remainders are unequal. VI. Things which are double of the same or equal, things, are equal. VII. Things which are halves of the same thing, are equal. VIII....
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 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 school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 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...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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...the wholes are equal. in. 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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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...equal. in. If equals he taken from equals, the remainders are equal. IV. If equals he added to nnequals, the wholes are unequal. V. If equals be taken from...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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 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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