Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical ProblemsIvison, Phinney, Blakeman & Company, 1865 - 444 Seiten |
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Seite 88
... the general definitions of Geometry , but it was deemed advisable to reinsert them here . 7. A Chord of a circle is the line connecting 88 GEOMETRY . BOOK III Of the Circle, and the Investigation of Theorems dependent on Properties.
... the general definitions of Geometry , but it was deemed advisable to reinsert them here . 7. A Chord of a circle is the line connecting 88 GEOMETRY . BOOK III Of the Circle, and the Investigation of Theorems dependent on Properties.
Seite 89
... chord . Thus , in the last figure , EGF is an arc , and EF is a chord of the circle , and the spaces bounded by the chord EF , and the two arcs EGF and EDF , into which it divides the circumference , are segments . 9. A Tangent to a ...
... chord . Thus , in the last figure , EGF is an arc , and EF is a chord of the circle , and the spaces bounded by the chord EF , and the two arcs EGF and EDF , into which it divides the circumference , are segments . 9. A Tangent to a ...
Seite 90
... chord , bisects the chord , and also the arc of the chord . Let AB be a chord , C the center of the circle , and CE a radius perpen- dicular to AB ; then we are to prove that AD = BD , and AE = EB . C D A B E Since C is the center of ...
... chord , bisects the chord , and also the arc of the chord . Let AB be a chord , C the center of the circle , and CE a radius perpen- dicular to AB ; then we are to prove that AD = BD , and AE = EB . C D A B E Since C is the center of ...
Seite 91
With Numerous Practical Problems Horatio Nelson Robinson. 2d . That the perpendicular to the chord at its middle ... chords . Let the angle ACE = the angle ECB ; then the two isosceles triangles , ACE , and ECB , are equal in all re ...
With Numerous Practical Problems Horatio Nelson Robinson. 2d . That the perpendicular to the chord at its middle ... chords . Let the angle ACE = the angle ECB ; then the two isosceles triangles , ACE , and ECB , are equal in all re ...
Seite 92
... chords in the same or equal circles , the one nearer the center is the greater . 2 = AG2 + The equation , EH2 + HC2 GC , being true ... chord that can be drawn in it . THEOREM IV . A line tangent to the circumference of 92 GEOMETRY .
... chords in the same or equal circles , the one nearer the center is the greater . 2 = AG2 + The equation , EH2 + HC2 GC , being true ... chord that can be drawn in it . THEOREM IV . A line tangent to the circumference of 92 GEOMETRY .
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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.