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 3
... square described upon any straight line AB , or the square of which A B is a side , is called the square of A B , or A B square . 21. The altitude of a parallelogram or triangle , is a perpendicular drawn to the base from the side or ...
... square described upon any straight line AB , or the square of which A B is a side , is called the square of A B , or A B square . 21. The altitude of a parallelogram or triangle , is a perpendicular drawn to the base from the side or ...
Page 16
... square : for , hence it appears , that a rhombus has all its sides equal to one another ; that a rectangle has all its angles right angles ; and that a square has all its sides equal , and all its angles right angles . PROP . 23. ( EUc ...
... square : for , hence it appears , that a rhombus has all its sides equal to one another ; that a rectangle has all its angles right angles ; and that a square has all its sides equal , and all its angles right angles . PROP . 23. ( EUc ...
Page 18
... square of that straight line , as often as is denoted by the product of the two numbers , which denote how often the line itself is contained in the two sides . Let A BDC be a rectangle , and let its adjacent sides AB , AC , contain ...
... square of that straight line , as often as is denoted by the product of the two numbers , which denote how often the line itself is contained in the two sides . Let A BDC be a rectangle , and let its adjacent sides AB , AC , contain ...
Page 19
... square of the aforesaid part . A C B Let the straight line A B be divided into any two parts AC , CB : the rec- tangle under AB , B C shall be equal to the rec- tangle under AC , CB , together with the square of B C. E Draw the straight ...
... square of the aforesaid part . A C B Let the straight line A B be divided into any two parts AC , CB : the rec- tangle under AB , B C shall be equal to the rec- tangle under AC , CB , together with the square of B C. E Draw the straight ...
Page 20
... square of A B is less than the square of AC by the square of B C , together with twice the rectangle AB , BC . Therefore , the same square of A B is less than the squares of A C , B C , by twice the square of BC , together with twice ...
... square of A B is less than the square of AC by the square of B C , together with twice the rectangle AB , BC . Therefore , the same square of A B is less than the squares of A C , B C , by twice the square of BC , together with twice ...
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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