Elements of Geometry, Plane and Spherical Trigonometry and Conic SectionsJ. Ernst, 1854 - 335 Seiten |
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Seite 61
... chord . 6. The space on either side of a chord , inclosed by the chord and arc , is called a segment of a circle . 7. Any chord which passes through the center , is called a diameter , and such a chord divides the circle into two equal ...
... chord . 6. The space on either side of a chord , inclosed by the chord and arc , is called a segment of a circle . 7. Any chord which passes through the center , is called a diameter , and such a chord divides the circle into two equal ...
Seite 62
... chord . Let AB be a chord , C the center of the circle , and CD perpendicular to AB ; then we are to prove that AD = BD , and AE = EB . D B E As C is the center of the circle , AC CB , and CD is common to the two As ACD and BCD , and ...
... chord . Let AB be a chord , C the center of the circle , and CD perpendicular to AB ; then we are to prove that AD = BD , and AE = EB . D B E As C is the center of the circle , AC CB , and CD is common to the two As ACD and BCD , and ...
Seite 63
... chords equally distant from the center , are equal . Equation ( 3 ) is true , under all circumstances , and if we suppose C greater than c , then P will be less than p ; that is , the greater the chord , the nearer it will be to the ...
... chords equally distant from the center , are equal . Equation ( 3 ) is true , under all circumstances , and if we suppose C greater than c , then P will be less than p ; that is , the greater the chord , the nearer it will be to the ...
Seite 64
... chords subtend or stand on equal portions of the circumference . Conceive two equal circles , and two equal chords ... chord is bisected by a line at right angles , the bisecting line will pass through the center of the circle ( th . 1 ...
... chords subtend or stand on equal portions of the circumference . Conceive two equal circles , and two equal chords ... chord is bisected by a line at right angles , the bisecting line will pass through the center of the circle ( th . 1 ...
Seite 68
... chord , is measured by one half of the intercepted arc . Let AB be a tangent , and AD a chord , and A the point of contact ; then we are to show that the angle BAD is measured by half the arc AED . From A , draw the radius AC ; and from ...
... chord , is measured by one half of the intercepted arc . Let AB be a tangent , and AD a chord , and A the point of contact ; then we are to show that the angle BAD is measured by half the arc AED . From A , draw the radius AC ; and from ...
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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