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" Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles. "
The first three books of Euclid's Elements of geometry, with theorems and ... - Side 17
av Euclid, Thomas Tate - 1849 - 108 sider
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...the one equal to the three sides of the other, each to each, are equul in all respects . . 7 (•7) Any two angles of a triangle are together less than two right angles 7 (A} A triangle cannot have more than one right angle, or more than one obtuse angle . . nor. 7 (i)...
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On the study and difficulties of mathematics [by A. De Morgan].

Augustus De Morgan - 1831
...than two right angles, is not an assumption but a consequence of his proposition, which shews that any two angles of a triangle are together less than two right angles, and which is established before any mention is made of parallels. It has been found by the experience...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 sider
...the angle ACD, is greater than the angle ABC. Therefore if one side, &c. QED PROP. XVII. THEOR. Jlny two angles of a triangle are together less than two...exterior angle of the triangle ABC, ACD is greater (16. 1.) than the interior and opposite angle ABC; to each of these add the angle ACB; therefore the...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833
...line. For then an external angle would be = to an internal and opposite, which is absurd. PROP. 17, THEOR. Any two angles of a triangle are together less than two right angles. Produce any side ; then the external angle is greater than either of the internal remote angles ; but...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 sider
...And by parity of reasoning, the like may be proved in every other triangle. Wherefore, universally, any two angles of a triangle are together less than two right angles. Which was to be demonstrated. COH. 1. A triangle cannot have more than one right angle; nor more than...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...side, &e. OED PROPOSITION XVII. THEOR. — Any two angles of a triangle are together lest than Iwo right angles. Let ABC be any triangle : any two of its angles together shall be less than two right angles. Produce BC to D : and because ACD is the exterior angle of the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 sider
...that the angle BCG, that is (8. 1.) the angle ACD, is greater than the angle ABC. PROP. X. THEOR. Aw) two angles of a triangle are together less than two...Produce BC to D ; and because ACD is the exterior ano-le of the triangle ABC, ACD is greater (9. 1.) than the interior and opposite angle ABC ; to each...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...d 15. 1. greater than the angle ABC. Therefore, " if one side" &c. QED PROP. XVII. THEOR. Any tico angles of a triangle are together less than two right...right angles. Produce BC to D ; and because ACD is the exteriorangle of the triangle ABC, ACD is greater3 than the interior and , opposite angle ABC; to each...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...Therefore, Sic. Cor. The two triangles are equal in every respect. (4. & 4 Cor.) PROP. 8. (Eue. i. 17.) Any two angles of a triangle are together less than two right angles. Let А В С be any triangle : any two of its angles, ABC and ACB, shall be together less than two right...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 471 sider
...that is1', the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. QED PROP. XVII. THEOR. Any two angles of a triangle are together less than two right angles. Book I. Let ABC be any triangle ; any two of its angles together are less than two right angles. Produce...
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