Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce Morton] 1830. Elements of trigonometry, by W. Hopkins. 1833. Elements of spherical trigonometry, by A. De Morgan. A treatise on algebraical geometry, by S.W. Waud. 1835Baldwin & Craddock, 1835 - Mathematics |
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Page 30
... scribed , which shall be equal to the dif- ference of two given rectilineal figures ( 58. Cor . ) . PROP . 60. Prob . 19 . To describe a square which shall be equal to the sum of two , three , or 30 [ 1.97 GEOMETRY .
... scribed , which shall be equal to the dif- ference of two given rectilineal figures ( 58. Cor . ) . PROP . 60. Prob . 19 . To describe a square which shall be equal to the sum of two , three , or 30 [ 1.97 GEOMETRY .
Page 44
... ference . For , since A : B :: C : D , componendo A + B : B :: C + D : D . And again , because invertendo B : A :: D : C , convertendo B : A - B :: D : C - D . Therefore , ex æquali A + B : A ~ B : : C + D : C - D , which is the ...
... ference . For , since A : B :: C : D , componendo A + B : B :: C + D : D . And again , because invertendo B : A :: D : C , convertendo B : A - B :: D : C - D . Therefore , ex æquali A + B : A ~ B : : C + D : C - D , which is the ...
Page 46
... ference ) , and if P be to Q always in the same given ratio of C to D , A shall be to B in the same ratio . First , let P and Q approach to A and B respectively by a continual increase , so that P and Q can never equal , much less ...
... ference ) , and if P be to Q always in the same given ratio of C to D , A shall be to B in the same ratio . First , let P and Q approach to A and B respectively by a continual increase , so that P and Q can never equal , much less ...
Page 64
... ference . Many other instances will occur in the remaining part of this treatise , in which the demonstrations are consider- ably abridged by the use of this very important theorem . We shall conclude the present Scho- lium by applying ...
... ference . Many other instances will occur in the remaining part of this treatise , in which the demonstrations are consider- ably abridged by the use of this very important theorem . We shall conclude the present Scho- lium by applying ...
Page 65
... ference of the squares of BA , AC is equal to the difference of the squares of BD , DC ( I. 38. ) or , which is the same thing ( 1.34 . ) , the rectangle under the sum and difference of BA , AC is equal to the rectangle under the sum ...
... ference of the squares of BA , AC is equal to the difference of the squares of BD , DC ( I. 38. ) or , which is the same thing ( 1.34 . ) , the rectangle under the sum and difference of BA , AC is equal to the rectangle under the sum ...
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Common terms and phrases
A B C ABCD adjacent angles altitude apothem base BC bisect centre chord circum circumference circumscribed coincide common measure common section compounded cone conic section contained convex surface cylinder describe a circle diameter dihedral angle divided draw drawn edges equal angles equimultiples ference fore four magnitudes frustum given point given straight line gles harmonical harmonical mean Hence hyperbola hypotenuse inscribed join likewise locus meet parallel parallelogram parallelopiped pass pendicular pentagon perimeter perpendicular plane prism Prob produced PROP proposition pyramid quadrilateral radii radius rallel rectangle rectilineal figure regular polygon respectively right angles Scholium scribed segment sides A B similar solid angles sphere spherical angle square of A B straight lines A B tangent third three sides touch triangle ABC vertex vertical