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" ANY two angles of a triangle are together less than two right angles. "
The Elements of Euclid - Side 20
av Euclid - 1838 - 416 sider
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Class lessons on Euclid

Marianne Nops - 1882
...is greater than L ABC. Prop. 17. A simple theorem follows this somewhat intricate demonstration : ' Any two angles of a triangle are together less than two right angles.' To show this we must compare them with two angles which either are or are together equal to two right...
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Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 96 sider
...on the base must fall without the triangle, towards the side on which is the obtuse angle. PROP. 17. THEOR. Any two angles of a triangle are together less than two right angles. Given A ABC. To prove any two of its angles, as LB + L ACB, < 2 Lr-s. Produce BC to D. •: L ACD >...
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Theories and Criticisms: Being Brief Essays on Metaphysical and Other Subjects

J. McD. Scott - 1883 - 94 sider
...shall, if produced, meet upon that side. This, it will be seen, is the converse of the proposition, that any two angles of a triangle are together, *less than two right angles. Neither postulate nor axiom is needed but once ; namely, to prove that lines which are parallel to...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...is produced, the exterior angle is greater than either of the interior opposite angles. THEOR. 10. Any two angles of a triangle are together less than two right angles. COR. 1. If a triangle has one right angle or obtuse angle, its remaining angles are acute. COR. 2....
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 sider
...or theorem; as for example, To describe an equilateral triangle on a given finite straight line, or Any two angles of a triangle are together less than two right angles. After the general enunciation follows the discussion of the proposition. First, the enunciation is...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1883
...given line ; the perpendicular will fall on the side of the acute angle. PROPOSITION XVII. THEOREM. Any two angles of a triangle are together less than two right angleg. c jo Let ABC be any A . Then must any two of its L s be together less than two rt. L s. Produce...
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The elements of plane geometry, Volum 1

Mathematical association - 1884
...of the angles of the triangle FBC is equal to the sum of the angles of the triangle ABC. TIIKOR. 10. Any two angles of a triangle are together less than two right angles. Let ABC be a triangle : then shall any two of its angles be together less than two right angles. Produce BC to...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - 1884
...of the angles of the triangle FBC is equal to the sum of the angles of the triangle ABC. THROB. 10. Any two angles of a triangle are together less than two right angles. Let ABC be a triangle : then shall any two of its angles be together less than two right angles. Produce BC to...
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Relfe brothers' Euclid sheets, propositions 1-26, book 1

Euclides - 1884
...SHEETS. PROPOSITIONS 1—26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS. PEOPOSITION XVII. Any two angles of a triangle are together less than two right angles. Let be any triangle. Then any two of its angles together shall be less than two right angles. Produce any...
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volum 1

Euclides - 1884
...by those sides equal to one another, they shall also have their bases or third sides equal. (8) 8. Any two angles of a triangle are together less than two right angles. (8) 9. The opposite sides and angles of a parallelogram are equal to one another. (9) 10. If two isosceles...
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