The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 9
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 . * 3 Ax , PROP . III . PROB . G * 2.1 . From the greater of two given straight lines to cut off a part equal ...
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 . * 3 Ax , PROP . III . PROB . G * 2.1 . From the greater of two given straight lines to cut off a part equal ...
Page 10
Therefore the base BC coincides with the base EF , and 18 Ax . therefore is equalt to it . Wherefore the whole triangle ABC coincides with the whole triangle : DEF , and is equal to it ; and the io EUCLID'S ELEMENTS . NÁ ...
Therefore the base BC coincides with the base EF , and 18 Ax . therefore is equalt to it . Wherefore the whole triangle ABC coincides with the whole triangle : DEF , and is equal to it ; and the io EUCLID'S ELEMENTS . NÁ ...
Page 15
1 . coincides with the base EF , the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore likewise the angle BAC coincides with the angle EDF , and is equal * to it . Therefore * 8 AX . if two triangles , & c .
1 . coincides with the base EF , the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore likewise the angle BAC coincides with the angle EDF , and is equal * to it . Therefore * 8 AX . if two triangles , & c .
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 ...
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Common terms and phrases
altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole
Bibliographic information
| Title | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
| Author | Euclid |
| Editors | Robert Simson, Samuel Maynard |
| Translated by | Robert Simson |
| Publisher | Longman, Orme, Brown, Green, and Longmans, 1838 |
| Original from | University of Iowa |
| Digitized | 13 Jul 2015 |
| Length | 328 pages |
| Export Citation | BiBTeX EndNote RefMan |