The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 167
... is to the remaining side of the " " first . " III . A straight line is said to be cut in extreme and mean ratio , when the whole is to the greater segment , as the greater segment is to the less . † 3 . 1 . IV . The altitude of 167 ...
... is to the remaining side of the " " first . " III . A straight line is said to be cut in extreme and mean ratio , when the whole is to the greater segment , as the greater segment is to the less . † 3 . 1 . IV . The altitude of 167 ...
Page 168
... altitude of any figure is the straight line drawn from its vertex perpendicular to the base . PROP . I. THEOR . Triangles and parallelograms of the same altitude are one to another as their bases . Let the triangles ABC , ACD , and the ...
... altitude of any figure is the straight line drawn from its vertex perpendicular to the base . PROP . I. THEOR . Triangles and parallelograms of the same altitude are one to another as their bases . Let the triangles ABC , ACD , and the ...
Page 169
... altitudes are one to another as their bases . Let the figures be placed so as to have their bases in the same straight line ; and having drawn perpendiculars from the vertices of the triangles to the bases , the straight line which ...
... altitudes are one to another as their bases . Let the figures be placed so as to have their bases in the same straight line ; and having drawn perpendiculars from the vertices of the triangles to the bases , the straight line which ...
Page 170
... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for the same reason , as the triangle CDE to the triangle ADE , so is CE to EA : therefore , as BD to DA , so is CE * 11.5 ...
... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for the same reason , as the triangle CDE to the triangle ADE , so is CE to EA : therefore , as BD to DA , so is CE * 11.5 ...
Page 254
... altitude , the insisting straight lines of which are terminated in the same straight lines in the plane opposite to the base , are equal to one another . Let the solid parallelopipeds AH , AK be upon the same base AB , and of the same ...
... altitude , the insisting straight lines of which are terminated in the same straight lines in the plane opposite to the base , are equal to one another . Let the solid parallelopipeds AH , AK be upon the same base AB , and of the same ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole