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" ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 376
by Rev. John Allen - 1822 - 494 pages
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ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...triangles in the figure ; that is, as many times as there are sides, less two. But this product is equal to twice as many right angles as the figure has sides, less four right angles. Cor. 1. The sum of the interior angles in a quadrilateral, is equal to two...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 324 pages
...triangles is equal to two right angles (Th. xvii) : hence, the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles about the point P is equal to four right angles (Th. ii. Cor. 4) ; and...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...from a point f within the figure to each of its angles. And, by the preceding proposition, all the angles of these triangles are equal to twice as many right angles as there are triangles, that is, as there are sides of the figure : and the same angles are equal to the...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...lines from a point F within the figure to each of its angles. And by the preceding proposition, all the angles of these triangles are equal to twice as many right angles as there are triangles, that is, as there are sides of the figure; and the same angles are equal to the...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 136 pages
...There are formed as many triangles as the figure has sides, therefore all their angles taken together are equal to twice as many right angles as the figure has sides (a) ; but the angles at the point F are together equal to four right angles (4), therefore all the...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich, Thomas Stephens Davies, Stephen Fenwick, William Rutherford - Mathematics - 1853
...together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. COR. 2. All the exterior angles of any rectilineal figure are together equal to four right angles....
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The popular educator, Volumes 5-6

Popular educator - 1854
...divide it into three equal parts. *"'t 3Fig. .42. No. 3. interior angles together with four right angles are equal to twice as many right angles as the figure has sides. Therefore all the interior angles together with all the exterior angles are equal (Ax. 1) to all the...
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A Manual for Practical Surveyors

E.W. Beans - 1854
...taken. If the entire survey has been made as above directed, the sum of all the internal angles will be equal to twice as many right angles as the figure has sides, diminished by four right angles. If this sum, as in practice will be likely to be the case, should...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 432 pages
...triangles in the figure ; that is, as many times as there are sides, less two. But this product is equal to twice as many right angles as the figure has sides, less four right angles. Cor. 1. The sum of the interior angles in a quadrilateral is equal to two right...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...interior angles of the figure together with four right angles. But it has been proved that all the angles of these triangles are equal to twice as many right angles as the figure has sides. Therefore all the angles of the figure together with four right angles are equal to twice as many right...
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