The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 8
... a given finite straight line . Let AB be the given straight line ; it is re- quired to describe an equilateral triangle upon AB . From the centre A , at the * Pos- distance AB , describe * the tulate . circle BCD , and from the centre B ...
... a given finite straight line . Let AB be the given straight line ; it is re- quired to describe an equilateral triangle upon AB . From the centre A , at the * Pos- distance AB , describe * the tulate . circle BCD , and from the centre B ...
Page 9
... straight +1 Ax . line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given straight lines to ...
... straight +1 Ax . line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given straight lines to ...
Page 15
... straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal † to EF . + Hyp ... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is ...
... straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal † to EF . + Hyp ... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is ...
Page 16
... straight line AF . Which was to be done . PROP . X. PROB . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is re- quired to divide it into two equal parts ...
... straight line AF . Which was to be done . PROP . X. PROB . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is re- quired to divide it into two equal parts ...
Page 17
... line makes with another straight line are equal to one another , each of them is called a right * * 10 Def . angle ; therefore each of the angles DCF , ECF is a right angle . Wherefore , from the given point C , in the given straight ...
... line makes with another straight line are equal to one another , each of them is called a right * * 10 Def . angle ; therefore each of the angles DCF , ECF is a right angle . Wherefore , from the given point C , in the given straight ...
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