Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsJ. Ballantyne and Company, 1811 - 500 páginas |
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Página 14
... PROP . V. PROB . To bisect a given angle . Let ABC be an angle which it is required to bisect . B In the side AB take any point D , and from BC cut off BE equal to BD ; join DE , on which construct the isosceles triangle DFE ( I. 1 ...
... PROP . V. PROB . To bisect a given angle . Let ABC be an angle which it is required to bisect . B In the side AB take any point D , and from BC cut off BE equal to BD ; join DE , on which construct the isosceles triangle DFE ( I. 1 ...
Página 15
... PROP . VII . PROB . To bisect a given finite straight line . On the given straight line AB , construct two isosceles trian- gles ( I. 1. ) ACB and ADB , and join their vertices C and D by a straight line cutting AB in the point E : AB ...
... PROP . VII . PROB . To bisect a given finite straight line . On the given straight line AB , construct two isosceles trian- gles ( I. 1. ) ACB and ADB , and join their vertices C and D by a straight line cutting AB in the point E : AB ...
Página 16
... PROP . IX . THEOR . Any two angles of a triangle are together less than two right angles . The two angles BAC and BCA of the triangle ABC are together less than two right angles . For produce the common side ́ AC . And , by the last ...
... PROP . IX . THEOR . Any two angles of a triangle are together less than two right angles . The two angles BAC and BCA of the triangle ABC are together less than two right angles . For produce the common side ́ AC . And , by the last ...
Página 17
... , therefore , acute . PROP . XI . THEOR . The angles at the base of an isosceles triangle are equal . The angles BAC and BCA at the base of the isosceles triangle ABC are equal . B B For draw ( I. 5. ) BD bisecting the BOOK I. 17.
... , therefore , acute . PROP . XI . THEOR . The angles at the base of an isosceles triangle are equal . The angles BAC and BCA at the base of the isosceles triangle ABC are equal . B B For draw ( I. 5. ) BD bisecting the BOOK I. 17.
Página 19
... PROP . XIV . THEOR . That side of a triangle is the greater which sub- tends a greater angle . If , in the triangle ABC , the angle CAB be greater than ACB ; its opposite side BC is greater than AB . For if BC be not greater than AB ...
... PROP . XIV . THEOR . That side of a triangle is the greater which sub- tends a greater angle . If , in the triangle ABC , the angle CAB be greater than ACB ; its opposite side BC is greater than AB . For if BC be not greater than AB ...
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Términos y frases comunes
ABCD adjacent angle ANALYSIS angle ABC angle ACB angle BAC base AC bisect centre chord circumference COMPOSITION conse consequently the angle contained angle decagon describe a circle diameter distance diverging lines draw equal to BC evidently exterior angle given circle given in position given point given ratio given space given straight line greater hence hypotenuse inflected inscribed intercepted intersection isosceles triangle join let fall likewise mean proportional Note opposite parallel perpendicular point G polygon porism PROB PROP proposition quently radius rectangle rhomboid right angles Scholium segments semicircle semiperimeter side AC similar sine square of AB square of AC straight line given tangent THEOR triangle ABC twice the square vertex vertical angle whence wherefore