The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 9
... wherefore AL and BC are each of them equal to BG : and things that are equal to the same thing are equal to one another ; therefore the straight +1 Ax . line AL is equal to BC . Wherefore from the given point A a straight line AL has ...
... wherefore AL and BC are each of them equal to BG : and things that are equal to the same thing are equal to one another ; therefore the straight +1 Ax . line AL is equal to BC . Wherefore from the given point A a straight line AL has ...
Page 10
... wherefore also the point C shall coincide with the point F , because the † Hyp . straight line AC † is equal to DF : but the point B was proved to coincide with the point E ; wherefore the base BC shall coincide with the base EF ...
... wherefore also the point C shall coincide with the point F , because the † Hyp . straight line AC † is equal to DF : but the point B was proved to coincide with the point E ; wherefore the base BC shall coincide with the base EF ...
Page 15
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal to it . Therefore * 8 Ax if two triangles , & c . Q. E. D. * * PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal ...
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal to it . Therefore * 8 Ax if two triangles , & c . Q. E. D. * * PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal ...
Page 17
... Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Which was to be done . COR . - By help of this problem , it may be demonstrated , that two straight lines cannot have a ...
... Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Which was to be done . COR . - By help of this problem , it may be demonstrated , that two straight lines cannot have a ...
Page 20
... Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . If two straight lines cut one another , the vertical , or opposite angles , shall be equal . Let the two straight lines AB , CD , cut one another in the point E : the angle ...
... Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . If two straight lines cut one another , the vertical , or opposite angles , shall be equal . Let the two straight lines AB , CD , cut one another in the point E : the angle ...
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