Elements of Geometry and Trigonometry |
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Page 24
... consequently , AG = DF ( Prop . V. Cor . ) . But by hypothesis AC = DF ; and therefore , AC = AG ( Áx . 1. ) . But the oblique line AC cannot be equal to AG , which lies nearer the perpendicular AB ( Prop . XV . ) ; therefore , BC and ...
... consequently , AG = DF ( Prop . V. Cor . ) . But by hypothesis AC = DF ; and therefore , AC = AG ( Áx . 1. ) . But the oblique line AC cannot be equal to AG , which lies nearer the perpendicular AB ( Prop . XV . ) ; therefore , BC and ...
Page 32
... consequently , equal to the sum of the interior angles plus the exterior angles . Taking from each the sum of the interior angles , and there remains the exterior angles , equal to four right angles . PROPOSITION XXVIII . THEOREM . In ...
... consequently , equal to the sum of the interior angles plus the exterior angles . Taking from each the sum of the interior angles , and there remains the exterior angles , equal to four right angles . PROPOSITION XXVIII . THEOREM . In ...
Page 40
... Consequently , the four quan- PROPOSITION XII . THEOREM . If four quantities are proportional , their squares or cubes will Let then will and For , or , and also be proportional . M : NP : Q , M2 : N2 :: P2 : Q2 M3 : N3 :: P3 : Q3 MxQ ...
... Consequently , the four quan- PROPOSITION XII . THEOREM . If four quantities are proportional , their squares or cubes will Let then will and For , or , and also be proportional . M : NP : Q , M2 : N2 :: P2 : Q2 M3 : N3 :: P3 : Q3 MxQ ...
Page 41
... consequently also to two segments : but the smaller one is always meant , unless the contrary is expressed . An inscribed triangle is one which , like BAC , BOOK III . 41 BOOK III The Circle and the Measurement of Angles,
... consequently also to two segments : but the smaller one is always meant , unless the contrary is expressed . An inscribed triangle is one which , like BAC , BOOK III . 41 BOOK III The Circle and the Measurement of Angles,
Page 44
... consequently , the angle ACD is equal EOG ( Book 1. Prop . X. ) . Now , placing the semicircle ADB on its equal EGF , since the angles ACD , EOG , are equal , it is plain that the radius CD will fall on the radius OG , and the point D ...
... consequently , the angle ACD is equal EOG ( Book 1. Prop . X. ) . Now , placing the semicircle ADB on its equal EGF , since the angles ACD , EOG , are equal , it is plain that the radius CD will fall on the radius OG , and the point D ...
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Common terms and phrases
adjacent altitude angle ACB ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 213 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 233 - It is, indeed, evident, that the negative characteristic will always be one greater than the number of ciphers between the decimal point and the first significant figure.
Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.