The Elements of Euclid |
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Page 18
... equi- angular . PROP . VI . THEOR . 099 .. IF two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . • " Let ABC be a triangle having the ...
... equi- angular . PROP . VI . THEOR . 099 .. IF two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . • " Let ABC be a triangle having the ...
Page 19
... equiangular triangle is also equilateral . b PROP . VII . THEOR . B b 4. 1 . C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base See ...
... equiangular triangle is also equilateral . b PROP . VII . THEOR . B b 4. 1 . C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base See ...
Page 103
... given straight line D which is not greater than the diameter of the circle . Which was to be done . PROP . II . PROB . IN a given circle to inscribe a triangle equiangular to a given triangle . Book IV . a 17. 3 . b 23. 1 OF EUCLID . 103.
... given straight line D which is not greater than the diameter of the circle . Which was to be done . PROP . II . PROB . IN a given circle to inscribe a triangle equiangular to a given triangle . Book IV . a 17. 3 . b 23. 1 OF EUCLID . 103.
Page 104
... equiangular to the triangle DEF , and it is inscribed in the circle ABC . Which was to be done . d PROP . III . PROB . 47th ABOUT a given circle to describe a triangle equi- angular to a given triangle . 1 Let ABC be the given circle ...
... equiangular to the triangle DEF , and it is inscribed in the circle ABC . Which was to be done . d PROP . III . PROB . 47th ABOUT a given circle to describe a triangle equi- angular to a given triangle . 1 Let ABC be the given circle ...
Page 105
... equiangular to the triangle DEF : and it is described about the circle ABC . Which was to be done .. PROP . IV . PROB . TO inscribe a circle in a given triangle . Let the given triangle be ABC ; it is required to inscribe a circle in ...
... equiangular to the triangle DEF : and it is described about the circle ABC . Which was to be done .. PROP . IV . PROB . TO inscribe a circle in a given triangle . Let the given triangle be ABC ; it is required to inscribe a circle in ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore