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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.
The elements of plane geometry; or, The first six books of Euclid, ed. by W ... - Σελίδα 21
των Euclides - 1863
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## A Manual for Practical Surveyors

E. W. Beans - 1854 - 114 σελίδες
...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...

## The Elements of geometry; or, The first six books, with the eleventh and ...

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...are equal (I. 32) to two right angles, and there are as many triangles in the figure as it has sides, all the angles of these triangles are equal to twice as many right angles as the figure has sides. But all the angles of these triangles are equal to the interior angles of the figure, viz. ABС, BСD,...

## A Treatise on Land Surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1855 - 436 σελίδες
...proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is equal to twice as many right angles, as the figure has sides less two ; since the figure can be divided into that number of triangles. Hence this common rule. "...

## The Popular Educator, Τόμος 5

1856 - 428 σελίδες
...figure together with four right angles. But it has been ployed that all the angles of these mangles are equal to twice as many right angles as the figure...Therefore all the angles of the figure together with four right angles are equal to twice as many right »ngles as the flgure has sides. Corollary 2. All...

## The geometry of the three first books of Euclid, by direct proof from ...

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...straight lines from a point F within the figure to each of the angles. And by the last proposition all the angles of these triangles are equal to twice as many right angles as there are triangles or sides to the figure. And the same angles are equal to the internal angles of...

## Elementary text book for young surveyors and levellers

Henry James Castle - 1856 - 220 σελίδες
...angles are the exterior angles of an irregular polygon ; and as the sum of all the interior angles are equal to twice as many right angles, as the figure has sides, wanting four ; and as the sum of all the exterior, together with all the interior angles, are equal...

## Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 σελίδες
...superposition. 3. Prove that all the internal angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides; and that all the external angles are together equal to four right angles. In what sense are these propositions...

## A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1856 - 478 σελίδες
...proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is equal to twice as many right angles, as the figure has sides less two ; since the figure can be divided into that number of triangles. Hence this common rule. "...

## Elements of Plane Geometry, Μέρος 1

Thomas Hunter - 1878 - 142 σελίδες
...other, the remaining angles must be equal. Cor. 2. The sum of all the interior angles of a polygon is equal to twice as many right angles as the figure has sides, minus four right angles. In the case of the triangle, this corollary has just been demonstrated; for,...

## Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879 - 474 σελίδες
...right angles, and there are as many triangles as the figure has sides ; therefore all the angles of all these triangles are equal to twice as many right angles as the figure has sides. But all the angles of all these triangles are equal to the interior angles of the figure, together...