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" If the distance between the centres of two circles is equal to the difference of their radii, the two circles will touch each other internally. "
SYLLABUS OF PLANE GEOMETRY - Side 34
1876
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ELEMENTARY GEOMETRY, WITH APPLICATIONS IN MENSURATION.

CHARLES DAVIS, L.L. D. - 1850
...of their radii CH, HD (Bk. I. Th. x) ; but this would be contrary to the supposition. THEOREM VII. If the distance between the centres of two circles is equal to the difference of their radii, the two circles will touch each other internally. Let C and D be the centres...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - 1850 - 216 sider
...of their radii CH, HD (Bk. I. Th. x) ; but this would be contrary to the supposition. THEOREM VII. If the distance between the centres of two circles is equal to the difference of their radii, the two circles will touch each other internally. Let C and D be the centres...
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ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...radii, the two circumfer'*..*ces will be exterior the one to the other. PROPOSITION XIV. THEOEEM. \f the distance between the centres of two circles is equal to the difference of their radii, the two circumferences will touch each other internally. f Let 0 and D be...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 432 sider
...their radii, the two circumferences will be exterior the one to the other. PROPOSITION XIV. THEOREM. If the distance between the centres of two circles is equal to the difference of their radii, the two circumferences will touch each other internally. Let C and D be...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - 1857 - 432 sider
...this triangle, CAD, also, CD<CA+AD (B. 1., p. 7), CD>DA-AC (B. 1., p. 7, a) PROPOSITION XIII. THEOREM. If the distance between the centres of two circles is equal to the sum of their radii, the circumferences will touch each other externally. Let C and D be the centres of two circles at a...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1870 - 319 sider
...the point of contact, the radius will be perpen, dicular to the tangent. THEOREM VI. If the dis/ance between the centres of two circles is equal to the sum of their radii, the two circles will timch each other externally. Of the Circle. Let C and D be the two centres, and...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1871 - 187 sider
...hypothesis : hence, they are tangent externally ; which was to be proved. PROPOSITION XIV. THEOREM. ff the distance between the centres of two circles is equal to the difference of their radii, one will be tangent to the other internally. m Let C and D be the centres...
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 201 sider
...AO' > BO'. To each add OA, »nd OA + AO' (or OO') > OA + BO'. PROPOSITION V. 185. Ttieorem.—When the distance between the centres of two circles is equal to the sum of their radii, the circumferences are tangent to each other externally. The point A, where M cuts the line joining...
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A Treatise on Special, Or Elementary Geometry

Edward Olney - 1872 - 239 sider
...AO' > BO'. To each add OA, and OA + AO' (or OO') > OA + BO'. PROPOSITION T. 185. Theorem. — When the distance between the centres of two circles is equal to the sum of their radii, the circumferences are tangent to each other externally. 89 N FIG. 146. The point A, where M cuts the...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1872 - 455 sider
...hypothesis : hence, they are tangent externally ; which was to be proved. PROPOSITION XIV. THEOREM. If the distance between the centres of two circles is equal to the difference of their radii, one will be tangent to the other internally. T.ct C and D be the centres...
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