Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page v
... Proportion , and its Application to Geometrical Investigations .... 59 BOOK III . Of the Circle , and the Investigation of Theorems dependent on its Properties ....... 88 BOOK IV . Problems in the Construction of Figures in 1 * ( v )
... Proportion , and its Application to Geometrical Investigations .... 59 BOOK III . Of the Circle , and the Investigation of Theorems dependent on its Properties ....... 88 BOOK IV . Problems in the Construction of Figures in 1 * ( v )
Page 58
... BD -AC - CD ; therefore by ( Th . 38 ) , we have AD × BD = AC2 — CD2 . By adding CD to each of these equals , we obtain AD × BD + CD3 = AC2 Hence the theorem . BOOK II . PROPORTION . DEFINITIONS AND EXPLANATIONS . THE 58 GEOMETRY .
... BD -AC - CD ; therefore by ( Th . 38 ) , we have AD × BD = AC2 — CD2 . By adding CD to each of these equals , we obtain AD × BD + CD3 = AC2 Hence the theorem . BOOK II . PROPORTION . DEFINITIONS AND EXPLANATIONS . THE 58 GEOMETRY .
Page 59
With Numerous Practical Problems Horatio Nelson Robinson. BOOK II . PROPORTION . DEFINITIONS AND EXPLANATIONS . THE word Proportion , in its common meaning , de- notes that general relation or symmetry existing between the different ...
With Numerous Practical Problems Horatio Nelson Robinson. BOOK II . PROPORTION . DEFINITIONS AND EXPLANATIONS . THE word Proportion , in its common meaning , de- notes that general relation or symmetry existing between the different ...
Page 60
... Proportion is a formal statement of the equality of two ratios . Thus , if we have the four magnitudes A , B , C and ... proportion are the magnitudes , or more properly the representatives of the magnitudes compared . 5. The Extremes of ...
... Proportion is a formal statement of the equality of two ratios . Thus , if we have the four magnitudes A , B , C and ... proportion are the magnitudes , or more properly the representatives of the magnitudes compared . 5. The Extremes of ...
Page 61
... proportion are its first and third terms . 9. The Consequents of a proportion are its second and fourth terms . In expressing the equality of ratios in the form of a proportion , we may make the denominators the ante- cedents , and the ...
... proportion are its first and third terms . 9. The Consequents of a proportion are its second and fourth terms . In expressing the equality of ratios in the form of a proportion , we may make the denominators the ante- cedents , and the ...
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Common terms and phrases
ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.c Cosine Cotang diagonal diameter dicular difference distance divided draw equal angles equation equiangular equivalent find the angles four magnitudes frustum given line greater half Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles less Let ABC logarithm measured multiplied N.sine number of sides opposite angles 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 square straight line Tang tangent three angles three sides triangle ABC triangular prisms Trigonometry vertex vertical angle volume
Popular passages
Page 322 - 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.