Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 páginas |
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Página 21
... . 8. ) greater than ACD or ACB ; wherefore the angle CAB is much greater than ACB . r PROP . XIII . THEOR . That side of a triangle is the greater which sub- tends a greater angle . 1 If , in the triangle ABC , the angle CAB BOOK I. 21.
... . 8. ) greater than ACD or ACB ; wherefore the angle CAB is much greater than ACB . r PROP . XIII . THEOR . That side of a triangle is the greater which sub- tends a greater angle . 1 If , in the triangle ABC , the angle CAB BOOK I. 21.
Página 42
... Wherefore the triangles ADH and DEM , having two angles respectively equal and the inter- jacent sides AD , DE - are ( I. 20. ) equal , and consequent- ly AH is equal to DM . In the same manner , the tri- angle ADH is proved to be equal ...
... Wherefore the triangles ADH and DEM , having two angles respectively equal and the inter- jacent sides AD , DE - are ( I. 20. ) equal , and consequent- ly AH is equal to DM . In the same manner , the tri- angle ADH is proved to be equal ...
Página 44
... Wherefore EB , being equal to AC ( I. 26. ) which is equal to DF , is itself e- qual to DF . Add BD to each , A C and ED is equal to BF ; but EA is equal to BС ( І. 26. ) , and the interior angle AED is equal to the exterior angle CBF ...
... Wherefore EB , being equal to AC ( I. 26. ) which is equal to DF , is itself e- qual to DF . Add BD to each , A C and ED is equal to BF ; but EA is equal to BС ( І. 26. ) , and the interior angle AED is equal to the exterior angle CBF ...
Página 51
... Wherefore the rectangle contained by the altitude of the A trapezoid and half the sum of its pa- B C G E F D rallel sides , is equivalent to the rhomboid BF ( II . 1. cor . ) ; but the rhomboid EG is equivalent to the triangle ECD ( II ...
... Wherefore the rectangle contained by the altitude of the A trapezoid and half the sum of its pa- B C G E F D rallel sides , is equivalent to the rhomboid BF ( II . 1. cor . ) ; but the rhomboid EG is equivalent to the triangle ECD ( II ...
Página 52
... Wherefore B 1 the triangles ABC and AFK , thus having two an- A N C gles of the one respectively equal to those of the other , and the interjacent side AF equal to AB , are equal ( 1. 20. ) , and consequently the side AC is equal to AK ...
... Wherefore B 1 the triangles ABC and AFK , thus having two an- A N C gles of the one respectively equal to those of the other , and the interjacent side AF equal to AB , are equal ( 1. 20. ) , and consequently the side AC is equal to AK ...
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Otras ediciones - Ver todas
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD adjacent angle altitude angle ABC angle ADB angle BAC angle BCD base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle Geometry greater half Hence hypotenuse inscribed intercepted isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sinAC sinB sine square of AB square of AC tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Pasajes populares
Página 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Página 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Página 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Página 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Página 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Página 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Página 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Página 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.