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" Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another. "
Elements of geometry, based on Euclid, books i-iii - Page 9
by Edward Atkins - 1876 - 119 pages
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 pages
...same parallels EC, AG, therefore the parallelogram FECG is double of the triangle AEC j (1.41) but ' things which are double of the same are equal to one another ' (ax. C) therefore the parallelogram FECG is equal to the triangle ABC, and it has one of its angles...
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863 - 74 pages
...unequals, the wholes are unequal. •I. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one...are halves of the same, are equal to one another. II. The Five Axioms, which apply especially to magnitude^ are peculiarly AXIOMS OF GEOMETBT: 8. Magnitudes...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...uuequals, the remainders are unequal. 7. Things which are halves of the same, are equal to one another. 6. Things which are double of the same, are equal to one another. 8. Magnitudes which coincide with one another, that which is exactly fill the same space, are equal...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...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. vn. Things which are halves of the same, are equal to one another. vin. Magnitudes which coincide with...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...nnequals, 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. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...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. vn. Things which are halves of the same, are equal to one another. vm. Magnitudes which coincide with...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exag^ly...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...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. VII. Things which are halves of the same, are equal to one another. VEIL Magnitudes which coincide...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870 - 270 pages
...unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same, are equal to...are halves of the same, are equal to one another. II. The Five Axioms, which apply especially to magnitude, are peculiarly Axioms of Geometry. 8. Magnitudes...
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