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" IF the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base; the segments of the base shall have the same ratio which the other sides of the triangle have to one another... "
The Principles of the Solution of the Senate-house 'riders,' Exemplified by ... - Seite 9
von Francis James Jameson - 1851 - 116 Seiten
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 488 Seiten
...parallels f ; therefore DE is parallel to BC. Wherefore if a ftraight line, &c. Q^ED PROP. III. THE OR. TF the angle of a triangle be divided into two equal angles, by a ftraight line which alfo cuts the bafe ; the fegments of the bafe fhall have the fame ratio which the...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 534 Seiten
...parallels e ; therefore DE is parallel no BC. Wherefore, if a ftraight line, &c, Q^ED PRO P. HI- THEO R. IF the angle of a triangle be divided into two equal angles, by a ftraight line which alfo cuts the bale i the fegments of the bafe mall have the fame ratio which the...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1781 - 534 Seiten
...parallels f ; therefore DE is parallel to BC. Wherefore if a ftraight line, &c. Q^ ED PROP. III. THEO R. IF the angle of a triangle be divided into two equal angles, by a ftraight line which alfo cuts the bafe ; the fcgments of the bafe (hall have the fame ratio which the...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 Seiten
...parallels s ; therefore DE is parallel to BC. Wherefore, if a ftraight line, &c. PROP. III. THEO R. IF the angle of a triangle be divided into two equal angles, by a ftraight line which alfo cuts the bafe ; rhe legments of the bafe fhall have the fame ratio which the...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 374 Seiten
...parallels s ; therefore DE is parallel to BC. Wherefore, if a ftraight line, &.c. C^ ED PROP. III. THEOR. IF the angle of a triangle be divided into two equal angles, by a ftraight line which alfo cuts the bale ; the fegments of the bafe mall have the fame ratio which the...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804 - 530 Seiten
...therefore DE is paralle} to BCJ, Wherefore if a ftraight line, &c. Q^E, D. ..»r •»• PROP. |II. THEOR. IF the angle of a triangle be divided into two equal angles, by a ftraight line which alfo cuts the bafe ; the fegments of the bafe mail have the fame ratio which the...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 Seiten
...angle, fcc. QED PROP. A. THEOR. IF the outward angle of a triangle, made by producing one of its sides, be divided into two equal angles, by a straight line which also cuts the base produced; the segments between the dividing line and the extremities of the base have the same ratio...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 Seiten
...which may be inferred from 11. 5. PROP. III. THEOR. Book VI. IF the angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base will have the same ratio which the other sides of the triangle have to each other ; and if the segments...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 554 Seiten
...therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROP. III. THEOR. See Note. IF the angle of a triangle be divided into two equal...which also cuts the base; the segments of the base shall have the same ratio which the other sides of the triangle have to one another: and if the segments...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Band 5

John Mason Good - 1813 - 714 Seiten
...equal anglrs. Prop. A. Theor. If the outward angle of a tri. angle made by producing OOP of its sides, be divided into two equal angles, by a straight line which also cuts the base produced; the segments one angle in the one eqaal to one angle in the other, and their bides about...
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