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 TrigonometryW.E. Dean, 1839 - 318 σελίδες |
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Σελίδα 22
... straight lines ( 1. Post . ) CA , CB to the points A , B ; ABC is an equilateral triangle . C D B E A Because the point A is the centre of the circle BCD , AC is equal ( 11. Definition ) to AB ; and because the point B is the centre of ...
... straight lines ( 1. Post . ) CA , CB to the points A , B ; ABC is an equilateral triangle . C D B E A Because the point A is the centre of the circle BCD , AC is equal ( 11. Definition ) to AB ; and because the point B is the centre of ...
Σελίδα 23
... A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done . 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 ...
... A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done . 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 ...
Σελίδα 24
... A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal equal to the angle EDF ...
... A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal equal to the angle EDF ...
Σελίδα 27
... straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to EF : there- fore BC coinciding with EF , BA and AC shall coincide with ED , and DF ; for if BA , and CA do not coincide with ED , and ...
... straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to EF : there- fore BC coinciding with EF , BA and AC shall coincide with ED , and DF ; for if BA , and CA do not coincide with ED , and ...
Σελίδα 28
... line , that is , to divide it into two equal parts . Let AB be the given ... AC is equal to CB , and CD common to the two triangles ACD , BCD : the two sides AC , CD , are equal to the two BC , CD , each to ... a straight 28 ELEMENTS.
... line , that is , to divide it into two equal parts . Let AB be the given ... AC is equal to CB , and CD common to the two triangles ACD , BCD : the two sides AC , CD , are equal to the two BC , CD , each to ... a straight 28 ELEMENTS.
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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 meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism produced proportional 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 parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore