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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 29
... PROP . XXXIV . THEOR . B D E Equivalent triangles on the same side of bases which are equal and in the same straight line , are between the same parallels . Let the equal triangles ABC , DEF be upon equal bases BC , EF , in the same ...
... PROP . XXXIV . THEOR . B D E Equivalent triangles on the same side of bases which are equal and in the same straight line , are between the same parallels . Let the equal triangles ABC , DEF be upon equal bases BC , EF , in the same ...
Página 31
... PROP . XXXVIII . THEOR . If the square described upon one of the sides of a triangle , be equivalent to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . If the square ...
... PROP . XXXVIII . THEOR . If the square described upon one of the sides of a triangle , be equivalent to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . If the square ...
Página 33
... PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part ...
... PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part ...
Página 34
... PROP . V. PROB . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is required to divide it into two equal parts . Describe ( Prob . 1. ) upon it an equilateral ...
... PROP . V. PROB . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is required to divide it into two equal parts . Describe ( Prob . 1. ) upon it an equilateral ...
Página 36
... PROP . IX . PROB . At a given point in a given straight line , to make a rectilineal angle equal to a given rectilineal angle . Let AB be the given straight line , and A the given point in it , and DCE the given rectilineal angle ; it ...
... PROP . IX . PROB . At a given point in a given straight line , to make a rectilineal angle equal to a given rectilineal angle . Let AB be the given straight line , and A the given point in it , and DCE the given rectilineal angle ; it ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore