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" Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. "
The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick - Side 4
av Royal Military Academy, Woolwich - 1853
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 138 sider
...same, are equal to one another. 7. Things which are halves of the same, are equal to one another. i 8. Magnitudes which coincide with one another, that is,...greater than its part. 10. Two straight lines cannot inclose a space. II. All right angles are equal. 12. .If a straight line meets two straight lines so...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 210 sider
...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,...one another. 9. The whole is greater than its part. A. The whole is equal to all its parts taken together. ED. B. It is impossible for the same thing to...
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The Works of Dugald Stewart: Elements of the philosophy of the human mind

Dugald Stewart - 1829 - 418 sider
...proper place. Kal ra 'upagpH-mira i«* aXXuXa Tffa a^AnAo/; irrl : — thus translated by Dr. Simson : " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This, in truth/is not an axiom, but a definition. It is the definition of geometrical equality ; the...
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The Works of Dugald Stewart: Elements of the philosophy of the human mind

Dugald Stewart - 1829 - 442 sider
...place. K«J rx lfieiift%cvrK 'or aXAnXai latt gXXifcui; Irrl '• — thus translated by Dr. Simson : " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality ; the...
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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - 1830 - 274 sider
...greater than any one of its parts. TRUTH VI. The sum of all the parts is equal to the whole. TRUTH VII. Magnitudes, which coincide with one another, that...exactly fill the same space, are equal to one another. TRUTH VIII. Between two points only one straight line can be drawn. TRUTH IX. The straight line is...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1831 - 166 sider
...same, are equal to one another. 7. Things which are halves of the same, are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to 1 one another. 9. The whole is greater than its part. 10. Two straight lines cannot inclose a space....
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Elements of Mental Philosophy: Abridged and Designed as a Text Book for ...

Thomas Cogswell Upham - 1832 - 622 sider
...the same, are equal to one another ; Things which are halves of the same, are equal to one another ; Magnitudes, which coincide with one another, (that...exactly fill the same space,) are equal to one another, &c. It will be admitted, (and we shall see it perhaps more clearly, when we again have occasion to...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 216 sider
...of the same or of equals, are equal to one another. 8. Magnitudes, which coincide with one another, are equal to one another. 9. The whole is greater than its part. 10. Two right lines cannot inclose a space. 11. All right angles are equal to one another. 12. If a right line...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Del 1

Francis Joseph Grund - 1834 - 202 sider
...greater than any one of its parts. TRUTH VI. The sum of all the parts is equal to the whole. TRUTH VII. . Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. TRUTH VIII. Between two points only one straight line can be drawn. TRUTH IX. The straight line is...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 sider
...are equal to one another. VII. Things which are halves of the same, arc equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, arc equal to one another. IX. The whole is greater than its part. X. Two straight lines cannot enclose...
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