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 páginas |
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Página 23
... fore , from the given point 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 ...
... fore , from the given point 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 ...
Página 27
... 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 FD , but have a different situation as EG and FG ; then , upon the same base EF , and upon the same side of it ...
... 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 FD , but have a different situation as EG and FG ; then , upon the same base EF , and upon the same side of it ...
Página 30
... fore because the straight line AB makes angles with the straight line CBE , upon one side of it , the an- gles ABC , ABE are together equal ( 13. 1. ) to two right angles ; but the angles ABC , ABD are likewise together equal to two ...
... fore because the straight line AB makes angles with the straight line CBE , upon one side of it , the an- gles ABC , ABE are together equal ( 13. 1. ) to two right angles ; but the angles ABC , ABD are likewise together equal to two ...
Página 31
... fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the point of their intersec- tion , are together equal to four right angles ...
... fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the point of their intersec- tion , are together equal to four right angles ...
Página 32
... fore the angles ACD , ACB are greater than the angles ABC , В ACB ; but ACD , ACB are to- A C D gather equal ( 13. 1. ) to two right angles ; therefore the angles ABC , BCA are less than two right angles . In like manner , it may be de ...
... fore the angles ACD , ACB are greater than the angles ABC , В ACB ; but ACD , ACB are to- A C D gather equal ( 13. 1. ) to two right angles ; therefore the angles ABC , BCA are less than two right angles . In like manner , it may be de ...
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Términos y frases comunes
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