Elements of Geometry and Trigonometry |
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Page 76
... described on the whole line is equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . Let AC be the line , and B the point of division ; then , is AC2 or ( AB + BC ) 2 ...
... described on the whole line is equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . Let AC be the line , and B the point of division ; then , is AC2 or ( AB + BC ) 2 ...
Page 178
... described by BC + CD , becomes the surface of the zone D described by the arc BCD : hence the sur- face of the zone is equal to EH × circ . OA . Scholium 2. When the zone has but one B F H OE base , as the zone described by the arc ABCD ...
... described by BC + CD , becomes the surface of the zone D described by the arc BCD : hence the sur- face of the zone is equal to EH × circ . OA . Scholium 2. When the zone has but one B F H OE base , as the zone described by the arc ABCD ...
Page 179
... described by ABC will , in that case , be the difference of the two cones described by ABD and ACD ; but at the same time , the cylinder de- B scribed by BCEF will be the difference ΕΑ C D of the two cylinders described by AFBD and AECD ...
... described by ABC will , in that case , be the difference of the two cones described by ABD and ACD ; but at the same time , the cylinder de- B scribed by BCEF will be the difference ΕΑ C D of the two cylinders described by AFBD and AECD ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC 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 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop 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 TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex