The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 89
... segment , & c . Q. E. D. PROP . XXII . THEOR . The opposite angles of any quadrilateral figure inscribed in a circle ... segment CDAB ; and the angle ACB is equal to the angle AĎB , because A they are in the same segment ADCB : therefore ...
... segment , & c . Q. E. D. PROP . XXII . THEOR . The opposite angles of any quadrilateral figure inscribed in a circle ... segment CDAB ; and the angle ACB is equal to the angle AĎB , because A they are in the same segment ADCB : therefore ...
Page 90
... segments of circles upon the equal straight lines AB , CD : the segment AEB shall be equal to the segment CFD . For if the segment AEB be applied to the segment CFD , so that the point A may be on C , and A A B C the straight line AB ...
... segments of circles upon the equal straight lines AB , CD : the segment AEB shall be equal to the segment CFD . For if the segment AEB be applied to the segment CFD , so that the point A may be on C , and A A B C the straight line AB ...
Page 91
... segment CFD , and therefore is equal to it . Wherefore similar segments , † 8 Ax , & c . Q. E. D. PROP . XXV . PROB . A segment of a circle being given , to describe the circle of which it is the segment . Let ABC be the given segment ...
... segment CFD , and therefore is equal to it . Wherefore similar segments , † 8 Ax , & c . Q. E. D. PROP . XXV . PROB . A segment of a circle being given , to describe the circle of which it is the segment . Let ABC be the given segment ...
Page 92
... segment ABC , which is there- fore greater than a semicircle . Wherefore a segment of a circle being given , the circle is described of which it is a segment . Which was to be done . + See Fig . 2 . + Sce PROP . XXVI . THEOR . In equal ...
... segment ABC , which is there- fore greater than a semicircle . Wherefore a segment of a circle being given , the circle is described of which it is a segment . Which was to be done . + See Fig . 2 . + Sce PROP . XXVI . THEOR . In equal ...
Page 93
... segment EDF ; and they are upon equal straight lines BC , EF : but similar segments of circles upon equal straight lines are equal * * 24 . 3 . to one another , therefore the segment BAC is equal to the segment EDF : but the whole ...
... segment EDF ; and they are upon equal straight lines BC , EF : but similar segments of circles upon equal straight lines are equal * * 24 . 3 . to one another , therefore the segment BAC is equal to the segment EDF : but the whole ...
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