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" Any two angles of a triangle are together less than two right angles. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Page 70
by Thomas Perronet Thompson - 1833 - 150 pages
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...Exercise- — From a point without a straight line, only one perpendicular can be drawn to it. PROP. XVII. THEOREM. Any two angles of a triangle are together less than two right angles. Let ABС be any triangle ; any two of its angles are together less than two right angles. Produce B С...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...two straight lines cut one another, the vertical or opposite angles shall be equal. The 17th, Book I. Any two angles of a triangle are together less than two right angles. The 18th, Book I. The greater side of every triangle is opposite to the greater angle. The 32nd, Book...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...reducing them to rectangular figures, these and similar conclusions are of great PROP. 17.— TMEOR. Any two angles of a triangle are together less than two right angles. CONSTRUCTION. — Pst. 2. A st. line may be produced to any length in a st. line. DEMONSTRATION. —...
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The Upper Canada Law Journal and Municipal and Local Courts' Gazette, Volume 4

Law - 1858 - 640 pages
...truths — its general principles — unchangeable and unchanged. When we enunciate the proposition that any two angles of a triangle are together less than two right angles, we enunciate an absolute truth in mathematics. When we enunciate the proposition that heat is always...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...ACD, (l. 15.) is greater than the angle ABC. Therefore, if one side of a triangle, &c. QED PKOPOSITION XVII. THEOREM. Any two angles of a triangle are together less than two right angles. Let ABC be any triangle. Then any two of its angles together shall be less than two right angles. Produce any...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...angle ABC ; therefore the exterior angle ACD is greater than either the angle CAB or ABC. PHOPOSmON XVII. THEOREM. Any two angles of a triangle are together less than two right angles. Given any triangle ABC ; to prove that any two of its angles together are less than two right angles....
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 pages
...that Is, the angle ACD, (r, 15) ls greater than the angle ABC. Therefore, if one side, &c. QED PROP. XVII. — THEOREM. Any two angles of a triangle are together less than two right angles (References — Prop. i. 13, 16; ax. 4.) Let ABC be any triangle. Then any two of its angles shall...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...that the angle BCG (or Us equal ACD), is greater than the angle ABC. PROPOSITION 17.— THEOREM. A ny two angles of a triangle are together less than two right angles. (References— Prop. I. 13, 16; ax. 4.) Hypothesis. — Let ABC be any triangle. Sequence. — Any...
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Responsions

University of Oxford - Education, Higher - 1863 - 328 pages
...line perpendicular to a given straight line of an unlimited length, from a given point without it. 3. Any two angles of a triangle are together less than, two right angles. 4. At a given point in a given straight line make a rectilineal angle equal to a given rectilineal...
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863 - 74 pages
...Therefore if one side of a triangle be produced, &e. QED Pitop. 17. — THEOE. (converse of Ax. 12.) Any two angles of a triangle are together less than two right angles. Con.— Pst. 2, DEJI.— P. 10, Ax. 4, P. 18. Let ABC be a triangle ; then any two /.s in it, as A...
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