Elements of Geometry, Plane and Spherical Trigonometry and Conic SectionsJ. Ernst, 1854 - 335 Seiten |
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Seite 140
... sine of 60 ° are each equal to the half of the radius . As Bn and EC are ... N , are right angles ; therefore , the AFHI , is equiangular , and similar ... cos.a = sin.b : FH. 140 ELEMENTS OF.
... sine of 60 ° are each equal to the half of the radius . As Bn and EC are ... N , are right angles ; therefore , the AFHI , is equiangular , and similar ... cos.a = sin.b : FH. 140 ELEMENTS OF.
Seite 145
... sine and cosine of 30 ° . The sine of 30 ° is ( prop . 1 , trig . ) , and , hence , cos . 230 ° —1—1 ( eq . ( 1 ) ... ( n ) ( n ) By adding ( m ) to ( n ) , and extracting square root , we obtain , cos . 150+ sin . 15 ° / 1.5 = 1.22474487 ...
... sine and cosine of 30 ° . The sine of 30 ° is ( prop . 1 , trig . ) , and , hence , cos . 230 ° —1—1 ( eq . ( 1 ) ... ( n ) ( n ) By adding ( m ) to ( n ) , and extracting square root , we obtain , cos . 150+ sin . 15 ° / 1.5 = 1.22474487 ...
Seite 148
... n B R : sin.A = b : CD ; or , R ( CD ) = b sin.A ( 1 ) By the similar As Bmn ... sine is radius . Scholium 2. When CB is less than AC , and the angle B ... sine of CB'D is the same as the sine of AB'C . In prac- tice we can determine ...
... n B R : sin.A = b : CD ; or , R ( CD ) = b sin.A ( 1 ) By the similar As Bmn ... sine is radius . Scholium 2. When CB is less than AC , and the angle B ... sine of CB'D is the same as the sine of AB'C . In prac- tice we can determine ...
Seite 152
... sine of any of the angles , as well as the cosine . It is done as follows : EQUATIONS FOR THE SINES OF THE ANGLES ... ( n ) . • · sin . + B = √√ sin.4 . S- -a S -C ac cb SC The preceding results are for radius unity ; for any 152 ELEMENTS OF.
... sine of any of the angles , as well as the cosine . It is done as follows : EQUATIONS FOR THE SINES OF THE ANGLES ... ( n ) . • · sin . + B = √√ sin.4 . S- -a S -C ac cb SC The preceding results are for radius unity ; for any 152 ELEMENTS OF.
Seite 154
... sin . A + sin.B : sin.A - sin . B - tan . 2 ( 4 + 3 ) : tan . ( 473 ) A - B This is equation ( 19 ) . In the triangle GnD , we have That is , 1 : 2sin . ( 4+ ) A - B = cos . 2 sin.90 ° : DG sin.nDG : Gn ; sin.nD G = cos.n GD A + B 2 : sin.A ...
... sin . A + sin.B : sin.A - sin . B - tan . 2 ( 4 + 3 ) : tan . ( 473 ) A - B This is equation ( 19 ) . In the triangle GnD , we have That is , 1 : 2sin . ( 4+ ) A - B = cos . 2 sin.90 ° : DG sin.nDG : Gn ; sin.nD G = cos.n GD A + B 2 : sin.A ...
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Elements of Geometry, Plane and Spherical Trigonometry, and Conic Sections Horatio Nelson Robinson Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
altitude angle ACB angle opposite angled spherical triangle base bisected chord circle circumference conceive cone conic section cos.a cos.b Cosine Cotang curve diameter difference distance divide draw ellipse equal angles equation equiangular figure find the angle foci frustum Geometry given line greater Hence hight hyperbola hypotenuse inscribed join less Let ABC line drawn logarithm major axis measured by half multiplied N.sine ordinate parabola parallel parallelogram parallelopipedon perpendicular polygon prism PROBLEM produced proportion pyramid Q. E. D. Cor Q. E. D. PROPOSITION Q. E. D. Scholium Q. E. D. THEOREM quantities radius rectangle represent right angled spherical right angled triangle right ascension right line secant segments semicircle sin.a sin.b sine sine and cosine solid solid angle sphere spherical trigonometry square straight line subtraction surface Tang tangent three angles triangle ABC trigonometry vertex vertical angle
Beliebte Passagen
Seite 62 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Seite 13 - AXIOMS. 1. Things which are equal to the same thing are equal to one another.
Seite 24 - If two triangles have two sides of the one equal to two sides of the...
Seite 149 - If a perpendicular be let fall from any angle of a triangle to its opposite side or base, this base is to the sum of the other two sides, as the difference of the sides is to the difference of the segments of the base.
Seite 48 - In place of adding unity, subtract it, and we shall find that a : a — b :: c : c — d. or a : b — a :: c : d — c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference.
Seite 110 - If a straight line stand at right angles to each of two straight lines in the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are.
Seite 21 - 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.
Seite 20 - If a side of a triangle be 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 together equal to two right angles.
Seite 47 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Seite 173 - I measured 312 yards in a right line by the side of the river, and then found that the two angles, one at each end of this line, subtended by the other end and the house, were 31° 15