Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical ProblemsIvison, Phinney, Blakeman & Company, 1865 - 444 Seiten |
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Seite 250
... b ; GI = cos.b. We are to find FM EP = = sin . ( a + b ) ; GM = cos . ( a + b ) ; sin . ( a - b ) ; GP = cos . ( a - b ) . Because IN is parallel to DO , the two △ ' s , GDO , GIN , are equiangular and similar . Also , the AFHI is ...
... b ; GI = cos.b. We are to find FM EP = = sin . ( a + b ) ; GM = cos . ( a + b ) ; sin . ( a - b ) ; GP = cos . ( a - b ) . Because IN is parallel to DO , the two △ ' s , GDO , GIN , are equiangular and similar . Also , the AFHI is ...
Seite 251
... cos.b + cos.a sin.b R By subtracting the second from the first , since IN - FH = IN — IK = EP , we have sin . ( a - b ) = sin.a cos.b cos.a sin.b R By subtracting the fourth from the third , we have GN - IH = GM = cos . ( a + b ) for ...
... cos.b + cos.a sin.b R By subtracting the second from the first , since IN - FH = IN — IK = EP , we have sin . ( a - b ) = sin.a cos.b cos.a sin.b R By subtracting the fourth from the third , we have GN - IH = GM = cos . ( a + b ) for ...
Seite 252
... B ) cos . ( AB ) ( 15 ) sin . A sin.B = 2cos . 2 A + B 2 B ) sin . ( 2 A - B ) ( 16 ) 2 cos . A + cos.B = 2cos . ( A + B ) cos . ( AB ) ( 17 ) 2 cos . B - cos . A 2sin . ( A + B ) sin . in . ( AB ) = 2 2 sin . ( 18 ) If we divide ...
... B ) cos . ( AB ) ( 15 ) sin . A sin.B = 2cos . 2 A + B 2 B ) sin . ( 2 A - B ) ( 16 ) 2 cos . A + cos.B = 2cos . ( A + B ) cos . ( AB ) ( 17 ) 2 cos . B - cos . A 2sin . ( A + B ) sin . in . ( AB ) = 2 2 sin . ( 18 ) If we divide ...
Seite 253
... cos . A cot . A 1 ( 27 ) 1 - cos . A tan . A tan . A sin . If we now turn back to formule ( A ) , and divide equa tion ( 7 ) by ( 9 ) , and ( 8 ) by ( 10 ) , observing at the same time that = tan . , we shall have , COS . sin.a cos.b + cos.
... cos . A cot . A 1 ( 27 ) 1 - cos . A tan . A tan . A sin . If we now turn back to formule ( A ) , and divide equa tion ( 7 ) by ( 9 ) , and ( 8 ) by ( 10 ) , observing at the same time that = tan . , we shall have , COS . sin.a cos.b + cos.
Seite 254
... cos.2a = 2sin2.a ( 32 ) The same hypothesis reduces equation ( 28 ) to 2tan.a tan.2a = 1 - tan2.a ( 33 ) If we ... B , C , and the sides opposite to them , by the small letters a , b , c . ) From either acute angle , as C , take ...
... cos.2a = 2sin2.a ( 32 ) The same hypothesis reduces equation ( 28 ) to 2tan.a tan.2a = 1 - tan2.a ( 33 ) If we ... B , C , and the sides opposite to them , by the small letters a , b , c . ) From either acute angle , as C , take ...
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Häufige Begriffe und Wortgruppen
2sin AB² ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.a cos.b cos.b cos.c Cosine Cotang diagonal diameter difference distance divided draw equal and parallel equal angles equation equiangular equivalent find the angles four magnitudes frustum given line greater Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles Let ABC logarithm measured multiplied N.sine number of sides parallelogram parallelopipedon pendicular perpen perpendicular plane ST polyedron PROB PROBLEM produced Prop proportion PROPOSITION prove pyramid quadrantal radii radius rectangle regular polygon right angles right-angled spherical triangle right-angled triangle SCHOLIUM secant segment similar sin.a sin.b sin.c sine solid angles sphere SPHERICAL TRIGONOMETRY straight line Tang tangent three angles three sides triangle ABC triangular prisms triedral angles Trigonometry vertex volume
Beliebte Passagen
Seite 318 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Seite 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 123 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Seite 58 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 29 - If one side of a triangle is produced, the exterior angle is equal to the sum of the two interior and opposite, angles; and the three interior angles of every triangle are equal to two right angles.
Seite 41 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Seite 96 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Seite 65 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Seite 77 - FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi.
Seite 113 - From a given point, to draw a line parallel to a given line. Let A be the given point, and BC the given line.