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" Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Σελίδα 40
των Euclid, Rev. John Allen - 1822 - 494 σελίδες
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Elements of the Geometry of Planes and Solids: With Four Plates

Ferdinand Rudolph Hassler - 1828 - 159 σελίδες
...angles, as AGD, GDE, and so on, standing in equal segments, are equal to one another; and their sum being equal to twice as many right angles as the figure has sides wanting four: that is, eight right angles, each of these angles of the hexagon is equal eight sixths...

The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 σελίδες
...right angles as the figure has sides ; but the internal angles, together with four right angles, are equal to twice as many right angles as the figure has sides (134). Take from both, the internal angles and the external remain equal to four right angles. %* This...

Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 σελίδες
...2rxn— 4r = (2n — 4) xr = (n— 2) x 2r, that is, all the interior angles of any convex rectilineal figure are together equal to twice as many right angles as the figure has sides less two sides. " Es. PROPOSITION M. THEOREM. All the exterior angles of any convex rectilineal figure,...

The London Encyclopaedia: Or, Universal Dictionary of Science, Art ..., Τόμος 10

Thomas Curtis - 1829
...BE. THEOREM XX. — All the interior angles of any rectilineal figure, А В С DE (fig. 43, p. I.), are together equal to twice as many right angles as the figure has sides wanting four right angles. For from any point, as F, within the figure, let lines be drawn to its angular...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 σελίδες
...equal to four right angles ; and the sum of its interior angles, together with four right angles, is equal to twice as many right angles as the figure has sides . . • 15 (¿•) The area of a rectilineal figure may be obtained by dividing it into triangles,...

The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833
...= to two right angles, (prop. 13.) Therefore, all the external angles, with all the internal, are = to twice as many right angles as the figure has sides ; but the internal angles, with four right angles, are = to twice as many right angles as the figure has sides;...

Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 σελίδες
...Therefore the other angles of the triangles, (which are together equal to all the interior •INIERC. 1. angles of the figure), are together* equal to twice as many right or> '' angles as the figure has sides, diminished by four right angles. Secondly; if the figure be...

The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 183 σελίδες
...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 angles (2); and therefore the angles of...

Inductive Geometry, Or, An Analysis of the Relations of Form and Magnitude ...

Charles Bonnycastle - 1834 - 631 σελίδες
...a result usually expressed as the following proposition : "The interior angles of any closed plane figure are together equal to twice as many right angles as the figure has sides, minus four right angles." 206. And as a second application of the principle in question, or, which...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 σελίδες
...QED COR. 1. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by...




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