The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 91
... Similar segments of circles are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle : it is required to find its centre . Draw within ...
... Similar segments of circles are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle : it is required to find its centre . Draw within ...
Página 113
... similar segments ACB , ADB , upon the same side of the same straight line AB , cannot but coincide . Wherefore , Upon the same , & c . Q. E. D. PROP . XXIV . THEOR . Similar segments of circles upon equal straight lines are equal to one ...
... similar segments ACB , ADB , upon the same side of the same straight line AB , cannot but coincide . Wherefore , Upon the same , & c . Q. E. D. PROP . XXIV . THEOR . Similar segments of circles upon equal straight lines are equal to one ...
Página 115
... similar to the segment EDF , and they are upon equal straight lines BC , EF : But similar seg- ments of circles upon equal straight lines are equal to one another ( 3.24 ) ; therefore the segment BAC is equal to the segment EDF : But ...
... similar to the segment EDF , and they are upon equal straight lines BC , EF : But similar seg- ments of circles upon equal straight lines are equal to one another ( 3.24 ) ; therefore the segment BAC is equal to the segment EDF : But ...
Página 140
... similar segments of circles be described , and from the extremities of the base tangents to the segment upon it be drawn to cut the other circumferences , the points of intersection and the vertex will be in the same line parallel to ...
... similar segments of circles be described , and from the extremities of the base tangents to the segment upon it be drawn to cut the other circumferences , the points of intersection and the vertex will be in the same line parallel to ...
Página 164
... to LC and CN . And it is evident that similar reasoning being applied to the triangles BHG , ADK will prove their perimeters equal to BN and BP with A₺ and AP . Therefore the sides of the three triangles cut off are 164 APPENDIX .
... to LC and CN . And it is evident that similar reasoning being applied to the triangles BHG , ADK will prove their perimeters equal to BN and BP with A₺ and AP . Therefore the sides of the three triangles cut off are 164 APPENDIX .
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