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 13
... hence the converse , because ( 14. Cor . 2. ) only one parallel can be drawn through the same point to the same straight line . That which is given in the text , however , seems preferable , as pointing out the connexion of the ...
... hence the converse , because ( 14. Cor . 2. ) only one parallel can be drawn through the same point to the same straight line . That which is given in the text , however , seems preferable , as pointing out the connexion of the ...
Page 29
... hence the passage is easy to the division of the rectilineal figure ; for it is evident ( 53. ) that , what- ever be the point L taken in AK , the figure A B CD N , constructed as above , will be equal to the triangle A B L , and will ...
... hence the passage is easy to the division of the rectilineal figure ; for it is evident ( 53. ) that , what- ever be the point L taken in AK , the figure A B CD N , constructed as above , will be equal to the triangle A B L , and will ...
Page 30
... hence a given triangle or rectilineal , figure may be divided into any number of equal parts , by straight lines drawn from a given point in one of its sides . PROP . 57. Prob . 16. ( Euc . i . 44. ) Upon a given base BD to describe a ...
... hence a given triangle or rectilineal , figure may be divided into any number of equal parts , by straight lines drawn from a given point in one of its sides . PROP . 57. Prob . 16. ( Euc . i . 44. ) Upon a given base BD to describe a ...
Page 31
... Hence a square may be de- scribed , which shall be equal to the sum of two , three , or any number of given rectilineal figures ( 58 Cor . ) . BOOK II . $ 1 . Ratios of Commensurable Magni- tudes - § 2. Proportion of Commen- surable ...
... Hence a square may be de- scribed , which shall be equal to the sum of two , three , or any number of given rectilineal figures ( 58 Cor . ) . BOOK II . $ 1 . Ratios of Commensurable Magni- tudes - § 2. Proportion of Commen- surable ...
Page 37
... hence that no other terms but such as are equimultiples of the lowest can express the same ratio ( 6. and 6. Cor . 1. ) ; which last simple relation given terms to the lowest terms , and affords an easy Rule for reducing any hence ...
... hence that no other terms but such as are equimultiples of the lowest can express the same ratio ( 6. and 6. Cor . 1. ) ; which last simple relation given terms to the lowest terms , and affords an easy Rule for reducing any hence ...
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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