Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page 50
... hypotenuse , and a side of the one equal to the hypotenuse and a side of the other , each to each , the two triangles are equal . Let ABC ard AGH be the two A's , in 50 GEOMETRY .
... hypotenuse , and a side of the one equal to the hypotenuse and a side of the other , each to each , the two triangles are equal . Let ABC ard AGH be the two A's , in 50 GEOMETRY .
Page 52
... hypotenuse AC , describe the square ACED . From D and E let fall the perpendiculars Db and Ed , on AB and AB ... hypotenuse AC of the one , is equal to the hypotenuse DE of the other . In like manner , it may be shown that the A's AbD ...
... hypotenuse AC , describe the square ACED . From D and E let fall the perpendiculars Db and Ed , on AB and AB ... hypotenuse AC of the one , is equal to the hypotenuse DE of the other . In like manner , it may be shown that the A's AbD ...
Page 53
... hypotenuse of a right - angled triangle , extract the square root of the sum of the squares of the two sides about the right angle . THEOREM XL . In any obtuse - angled triangle , the square on the side oppo- sive the obtuse angle is ...
... hypotenuse of a right - angled triangle , extract the square root of the sum of the squares of the two sides about the right angle . THEOREM XL . In any obtuse - angled triangle , the square on the side oppo- sive the obtuse angle is ...
Page 79
... hypotenuse . Also place C and D at right angles to each other , and draw the hypotenuse . Then bring the two triangles together , so that C shall be at right angles to B , as represented in the figure . A AD B BC C Now , these two A's ...
... hypotenuse . Also place C and D at right angles to each other , and draw the hypotenuse . Then bring the two triangles together , so that C shall be at right angles to B , as represented in the figure . A AD B BC C Now , these two A's ...
Page 86
... hypotenuse are in proportion to the squares on the adjacent sides of the triangle . 4. The sum of the squares on the two sides is equivalent to the square on the hypotenuse . Let BAC be a triangle , right an- gled at A ; and draw AD ...
... hypotenuse are in proportion to the squares on the adjacent sides of the triangle . 4. The sum of the squares on the two sides is equivalent to the square on the hypotenuse . Let BAC be a triangle , right an- gled at A ; and draw AD ...
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Common terms and phrases
ABē ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.b cos.c Cosine Cotang diagonal diameter dicular difference distance divided draw equal angles equation equiangular equivalent find the angle 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 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 subtracting Tang tangent three angles three sides triangle ABC triangular prisms triedral angles TRIGONOMETRY vertex vertical angle volume
Popular passages
Page 320 - 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 65 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 121 - 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 56 - 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 34 - Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle it itosceles.
Page 126 - To inscribe a regular polygon of a certain number of sides in a given circle, we have only to divide the circumference into as many equal parts as the polygon has sides : for the arcs being equal, the chords AB, BC, CD, &c.
Page 22 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Page 277 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 94 - 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 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.