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" ... twice as many right angles as the figure has sides. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Page 103
by Thomas Perronet Thompson - 1833 - 150 pages
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...triangles, is equal to two right angles (th. 17); therefore 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, which are so many many of the angles of the triangles,...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1812
...intvard angles, as the figure has sides : therefore the sum of all the inward and outward angles, is equal to twice as many right angles as the figure has sides. But the sum of all the inward angles, with four right angles, is equal to twice as many right angles as...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...adjacent esters, 1. rior ABD, is equal b to two right angles; therefore all the interior together with aH the exterior angles of the figure, are equal to twice as many right angles as there are sides |J" of the figure; that is, by the foregoing corollary, they are equal to all the interior...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...interior angle ABC, with its adjacent exterior ABD, is equal (13. 1.) to two right angles ; therefore all the interior, together with all the exterior angles...figure, are equal to twice as many right angles as there are sides of the fi- _ gure ; that is, by the fore- D going corollary, they are equal to all...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...many right angles as the figure has sides, wanting four. Fr. all the angles exterior and interior are equal to twice as many right angles as the figure has sides ; but the exterior are equal to four right angles ; therefore the interior are equal to twice as many right...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...two right angles [13. 1} ; therefore all the exterior and interior angles of the figure are together equal to twice as many right angles as the figure has sides ; but the interior angles are equal to twice as many right angles, except four, as the figure has sides [by...
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The First Six Books with Notes

Euclid - 1822 - 179 pages
...are formed as many triangles as the figure has sides, and, therefore, all their angles taken together are equal to twice as many right angles as the figure has sides ( 1 ), but the angles at the point F are equal to four right <z) Cor. 3. angles, (2), and therefore...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...; add all the inward angles A, n, c, &.c. together ; for when the work is right, their sum will be equal to twice as many right angles as the figure has sides, wanting 4 right angles. But when there is an angle, a* r, (hat bends inward*, and yon measure the external...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 508 pages
...to four right angles [Cor. 2. 15. 1] ; therefore the remaining angles, which constitute the interior angles of the figure, are equal to twice as many right angles, except four, as the figure has sides. V For every exterior, as ABD and its adjacent interior ABC, are...
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...twice as many right angles as the figure has sides ; or the interior angles of the figure, themselves, are equal to twice as many right angles as the figure has sides, wanting four right angles. QED Cor. 1. All the interior angles of any quadrilateral figure are together...
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