The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 18
... manner it may be demon- strated that no other can be in the same straight line with it but BD Therefore BD is in the same straight line with BC . Wherefore , If at a point , & c . Q. E. D. PROP . XV . THEOR . A E B D If two straight ...
... manner it may be demon- strated that no other can be in the same straight line with it but BD Therefore BD is in the same straight line with BC . Wherefore , If at a point , & c . Q. E. D. PROP . XV . THEOR . A E B D If two straight ...
Página 19
... manner , if the side BC be bisected and AC be produced to G , it may be demonstrated that the angle BCG , that is , the angle ACD ( 1. 15 ) , is greater than the angle ABC . Wherefore , If one side , & c . Q. E. D. PROP . XVII . THEOR ...
... manner , if the side BC be bisected and AC be produced to G , it may be demonstrated that the angle BCG , that is , the angle ACD ( 1. 15 ) , is greater than the angle ABC . Wherefore , If one side , & c . Q. E. D. PROP . XVII . THEOR ...
Página 20
... manner it may be demonstrated that the angles BAC , ACB , as also the angles CAB , ABC , are together less than two right angles . Wherefore , Any two angles , & c . Q. E. D. PROP . XVIII . THEOR . The greater side of every triangle is ...
... manner it may be demonstrated that the angles BAC , ACB , as also the angles CAB , ABC , are together less than two right angles . Wherefore , Any two angles , & c . Q. E. D. PROP . XVIII . THEOR . The greater side of every triangle is ...
Página 22
... manner it may be demonstrated that AB , BC , are greater than AC , and AC , CB , greater than AB . Wherefore , Any two sides , & c . Q. E. D. PROP . XXI . THEOR . If from the ends of a side of a triangle there be drawn two straight ...
... manner it may be demonstrated that AB , BC , are greater than AC , and AC , CB , greater than AB . Wherefore , Any two sides , & c . Q. E. D. PROP . XXI . THEOR . If from the ends of a side of a triangle there be drawn two straight ...
Página 28
... and opposite angle EFG ( 1. 16 ) : But it is also equal to it ( Hyp . ) which is impossible ; therefore AB and CD being produced do not meet towards B , D : And , in - like manner , it may be demonstrated that they do 28 EUCLID'S ELEMENTS .
... and opposite angle EFG ( 1. 16 ) : But it is also equal to it ( Hyp . ) which is impossible ; therefore AB and CD being produced do not meet towards B , D : And , in - like manner , it may be demonstrated that they do 28 EUCLID'S ELEMENTS .
Términos y frases comunes
AB² ABCD AC² AD² adjacent angles angle ABC angle ACB angle BAC angle equal base BC BC is equal centre chord circle ABC circumference diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given rectilineal given straight line gnomon hypotenuse inscribed intersection isosceles triangle join less Let ABC lines be drawn lines drawn meet multiple opposite angles parallel to BC parallelogram perpendicular plane polygon PROB produced proportionals Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment semicircle shew shewn square on AC tangents THEOR touches the circle triangle ABC twice the rectangle vertex Wherefore