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 51
... meet , if produced , towards B , D : let them meet in G , and join AG . Then because AC is equal to CE , the angle CEA is equal ( 3. 1. ) to the angle EAC ; and the angle ACE is a right angle ; therefore each of the angles CEA , EAC is ...
... meet , if produced , towards B , D : let them meet in G , and join AG . Then because AC is equal to CE , the angle CEA is equal ( 3. 1. ) to the angle EAC ; and the angle ACE is a right angle ; therefore each of the angles CEA , EAC is ...
Página 55
... meets the cir- cle , and being produced does not cut it . And that line which has but . one point in common with the ... meet , but do not cut one another . 4. Straight lines are said to be equally dis- tant from the centre of a circle ...
... meets the cir- cle , and being produced does not cut it . And that line which has but . one point in common with the ... meet , but do not cut one another . 4. Straight lines are said to be equally dis- tant from the centre of a circle ...
Página 57
... meet the circumference in F. Then , because DA is equal to DB , the angle DAB is equal ( 3. 1. ) to the angle DBA ; and because AE , a side of the triangle DAE , is produced to B , the angle DEB is greater ( 9. 1. ) than the angle DAE ...
... meet the circumference in F. Then , because DA is equal to DB , the angle DAB is equal ( 3. 1. ) to the angle DBA ; and because AE , a side of the triangle DAE , is produced to B , the angle DEB is greater ( 9. 1. ) than the angle DAE ...
Página 61
... meet in some point F ; for if they were parallel , the lines DB , CB , perpendicular to them would also be parallel ( Cor . 1. Th . 21. 1. ) , or else form but one straight line : but they meet in B , and ABC is not a straight line by ...
... meet in some point F ; for if they were parallel , the lines DB , CB , perpendicular to them would also be parallel ( Cor . 1. Th . 21. 1. ) , or else form but one straight line : but they meet in B , and ABC is not a straight line by ...
Página 62
... meet AB at equal distances from the perpendicular , they are equal . For similar reasons FB , FC , are equal ; hence the points A , B , C , are all equally distant from the point F , and con- sequently lie in the circumference of the ...
... meet AB at equal distances from the perpendicular , they are equal . For similar reasons FB , FC , are equal ; hence the points A , B , C , are all equally distant from the point F , and con- sequently lie in the circumference of the ...
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Términos y frases comunes
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