Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
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Page vii
... third Book , the remarks con- cerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has advanced no farther than the ele- ments of the science . The 27th , 28th ...
... third Book , the remarks con- cerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has advanced no farther than the ele- ments of the science . The 27th , 28th ...
Page ix
... Third Book , I have departed from EUCLID altogether , with a view of rendering it both shorter and more comprehensive . This , however , is not attempted by B introducing a mode of reasoning less rigorous than that of PREFACE . ix .
... Third Book , I have departed from EUCLID altogether , with a view of rendering it both shorter and more comprehensive . This , however , is not attempted by B introducing a mode of reasoning less rigorous than that of PREFACE . ix .
Page xv
... third ; it may be replied , that this is no doubt a truth which , without proof , most men will be inclined to admit ; but are we for that reason to account it of no consequence to know what the propositions are , which must cease to be ...
... third ; it may be replied , that this is no doubt a truth which , without proof , most men will be inclined to admit ; but are we for that reason to account it of no consequence to know what the propositions are , which must cease to be ...
Page 23
... third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite * D Let ABC , DEF be two triangles which have the ...
... third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite * D Let ABC , DEF be two triangles which have the ...
Page 33
... third side . Let ABC be a triangle ; any two sides of it together are greater than the third side , viz the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA'to the point D ...
... third side . Let ABC be a triangle ; any two sides of it together are greater than the third side , viz the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA'to the point D ...
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Common terms and phrases
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore