The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 129
... Tangents equal to two given straight lines are drawn from one point to two given circles : determine the point geometrically . Let AKL , CHM be the given circles : draw AC through their centres E , F ; at A and C let the given straight ...
... Tangents equal to two given straight lines are drawn from one point to two given circles : determine the point geometrically . Let AKL , CHM be the given circles : draw AC through their centres E , F ; at A and C let the given straight ...
Página 130
... tangents GH and GK being drawn ט M H and EK and FH joined , we have equal triangles BAE , GKE containing GK equal to AB , and similarly we have GH equal to DC . 5. Of all triangles on the same base , and having the same vertical angle ...
... tangents GH and GK being drawn ט M H and EK and FH joined , we have equal triangles BAE , GKE containing GK equal to AB , and similarly we have GH equal to DC . 5. Of all triangles on the same base , and having the same vertical angle ...
Página 132
... tangents be drawn to the circle , the squares on these tangents are together equal to the square on the straight line joining the points of intersection . Let ABCD be a quadrilateral inscribed in a circle , and having the sides BA , CD ...
... tangents be drawn to the circle , the squares on these tangents are together equal to the square on the straight line joining the points of intersection . Let ABCD be a quadrilateral inscribed in a circle , and having the sides BA , CD ...
Página 134
... tangent . 17. Shew that the two tangents to a circle , drawn from the same point without it , are equal to one another ; and hence prove that the sums of the opposite sides of any quadrilateral described about a circle are equal , and ...
... tangent . 17. Shew that the two tangents to a circle , drawn from the same point without it , are equal to one another ; and hence prove that the sums of the opposite sides of any quadrilateral described about a circle are equal , and ...
Página 135
... tangent at P cut AO at C , shew that AC = CP . 23. A common tangent is drawn to two circles which touch externally if a circle be described on that part of it which lies between the points of contact , as diameter , it will pass through ...
... tangent at P cut AO at C , shew that AC = CP . 23. A common tangent is drawn to two circles which touch externally if a circle be described on that part of it which lies between the points of contact , as diameter , it will pass through ...
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