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" THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. "
Elements of Geometry: Containing the First Six Books of Euclid: With a ... - Σελίδα 33
των John Playfair - 1819 - 317 σελίδες
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 σελίδες
...angle ABC greater than the angle ACB. Therefore the greater side, &c. QED PROPOSITION XIX. THEOREM. The greater angle of every triangle is subtended by the...which the angle ABC is greater than the angle BCA. Then the side AC shall be greater than the side AB. For, if AC be not greater than AB, AC must either...

The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - 1845 - 382 σελίδες
...Therefore, if two sides, &c. PROP. XIX. THEOR. — If two angles of a triangle be unequal, the greater angle has the greater side opposite to it. Let ABC be a triangle, of which the angle B is greater than C ; the side AC is likewise greater than AB. For if it be not greater, AC must either...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 σελίδες
...the angle ABC greater than the angle ACB. Wherefore, The greater side %c. QED PROP. XIX. THEOR. The greater angle of every triangle is subtended by the...triangle, of which the angle ABC is greater than the angle ACB : the side AC is also greater than the side AB. For, if it be not greater, it must either be equal...

The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846 - 128 σελίδες
...ACB, much more is /_ ABC > L ACB. Therefore the greater side, &c. PROP. XVIII. THEOR. 19. lEu. The greater angle of every triangle is subtended by the...greater side; or has the greater side opposite to it. If ABC be a ^, of which L ABC > L BCA; then AOAB. BC For AC must be either >, =, or < AB. 1st. If AC...

The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847 - 128 σελίδες
...ACB; and that as DC is > or < AC, the L BAC is > or < the / ABC. PROP. XIX. THEOR. GEN. ENUN. — The greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it. PART. ENUN. — Let ABC be a A, of which the Z ABC is > the Z ACB; then the side AC shall be > AB....

The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 σελίδες
...THEOREM. The greater side of every triangle is opposite to the greater angle. PROP. XIX. THEOREM. The greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it. PROP. XX. THEOREM. Any two sides of a triangle are together greater than the third side. PROP. XXI....

The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...is the angle ABC greater than ACB. Therefore the greater side, etc. QED PROPOSITION XIX. THEOR. The greater angle of every triangle is subtended by the...the angle BCA ; the side AC is likewise greater than tie side AB. For, if it be not greater, AC must either be equal to AB or less than it; it is not equal,...

The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Βιβλίο 1

Euclides - 1853 - 334 σελίδες
...then the side opposite to the greater angle shall be greater than the side opposite to the less angle. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA. Then the side AC shall be greater than the side AB. For if it be not greater, AC A must either be equal...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 176 σελίδες
...the angle abС than a С b. Therefore the greater side, <fee. QED PROPOSITION XIX. — THEOREM. The greater angle of every triangle is subtended by the greater side, or IMS tlie greater side opposite to it. LET abС be a triangle, of which the angle ab С is greater than...

Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - 1854 - 534 σελίδες
...side, &c. QED PROPOSITION XIX.— THEOREM. The greater angle of every triangle (А В С) is stdtended by the greater side, or has the greater side opposite to it. Let the angle В be greater than C; then AC shall be greater thanAB. О For, if it be not greater, AC must...




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