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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: With Practical Applications, for the Use of Schools - Page xiv
by Timothy Walker - 1829 - 129 pages
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Mensuration of lines, areas, surfaces, and volumes

Robert Rawson - 1856 - 200 pages
...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 same, are equal to one another. vin. Magnitudes which coincide with...
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Elements of Mental Philosophy: Embracing the Two Departments of ..., Volume 1

Thomas Cogswell Upham - Ethics - 1857 - 474 pages
...one another ; If equals be added to equals, the "wholes are equal; The whole is greater than a part; Things which are double of the same are equal to one another ; Things which are halves of the same are equal to one another ; Magnitudes which coincide with one...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be takea from unequals, the remainders are unequal. 6. Things...same, are equal to one another. 7. Things which are another. halves of the same, are equal to one II. The Five Axioms, which apply especially to magnitude,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 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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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
...equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. •I. If equals be taken from unequals, the remainders are...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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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 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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