The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 5
Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted , that a B 3 BOOK I. - DEFINITIONS . 5 o ...
Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted , that a B 3 BOOK I. - DEFINITIONS . 5 o ...
Page 30
Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CŨ . For , if it be not parallel , AB and CD being produced will meet either ...
Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CŨ . For , if it be not parallel , AB and CD being produced will meet either ...
Page 31
A G म * angle EGB equal to the interior and opposite angle GHD upon the same side ; or make the interior E angles on the same side BGH , GHD together equal B to two right angles : AB C-D shall be parallel to CD .
A G म * angle EGB equal to the interior and opposite angle GHD upon the same side ; or make the interior E angles on the same side BGH , GHD together equal B to two right angles : AB C-D shall be parallel to CD .
Page 32
Struight lines which are parallel to the sume straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD : and because GẮK cuts the ...
Struight lines which are parallel to the sume straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD : and because GẮK cuts the ...
Page 33
is equal to the angle GHF ; therefore also AGK is equal * to GKD : and they are alternate +1 Ax . angles ; therefore AB is parallel * to CD . * 27. 1 . Wherefore , straight lines , & c . Q. E. D. PROP . XXXI . PROB .
is equal to the angle GHF ; therefore also AGK is equal * to GKD : and they are alternate +1 Ax . angles ; therefore AB is parallel * to CD . * 27. 1 . Wherefore , straight lines , & c . Q. E. D. PROP . XXXI . PROB .
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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |
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 |