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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 First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852 - 152 pages
...will be able to draw any of the figures in this book.] 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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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 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 equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...any center, at any distance from that center. X 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. m. , If equals be taken from equals, the remainders are equal. IV. • If equals be added to unequals,...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 pages
...produced to any length in a straight line. III. 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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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...any eenter, at any distance from that center. 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. HI. If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...any centre, at any distance from that centre. AXIOMS. L Things -which are equal to the same thing, are equal to one another. II. If equals be added to equals, the wholes are equal. in. If equals he taken from equals, the remainders are equal. IV. If equals he added to nnequals, the...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...be produced to any length in a straight line. m. 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 unequal....
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...are the Postulates, to geometrical magnitudes. 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 and unequals be added together, the wholes...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872 - 216 pages
...propositions are called axioms. They are the following : — I. Magnitudes which are equal to the same, are equal to one another. II. If equals be added to equals, or if equals be added to the same, the sums will be equal. III. If equals be taken from, equals, or...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 592 pages
...be described from any centre, at any distance from that centre. AXIOMS. I. Things equal to the same are equal to one another. II. If equals be added to equals, the wholes arę equal. III. If equals be taken from equals, the remainder* are equal. IV. If equals be added to...
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