The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 23
... and it has been shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side .
... and it has been shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side .
Page 24
... CED are greatert than CD , add DB to each of therefore the sides CE , B † 4 Ax . EB , are greatert than CD , DB : but it has been shown that BA , AC are greater than BE , EC ; much more then are BA , AC , greater than BD , DC .
... CED are greatert than CD , add DB to each of therefore the sides CE , B † 4 Ax . EB , are greatert than CD , DB : but it has been shown that BA , AC are greater than BE , EC ; much more then are BA , AC , greater than BD , DC .
Page 28
1 . the base BC would be less * than the base EF : + Hyp . but it is t not ; therefore the angle BAC is not less than the angle EDF : and it was shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF .
1 . the base BC would be less * than the base EF : + Hyp . but it is t not ; therefore the angle BAC is not less than the angle EDF : and it was shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF .
Page 32
Again , because the straight A -B line GK cuts the parallel Н straight lines EF , CD , the E -F * 28 . 1. angle GHF is equal * to the CD angle GKD : and it was shown that the angle AGK >米 # is equal to the angle GHF ; therefore also 32 ...
Again , because the straight A -B line GK cuts the parallel Н straight lines EF , CD , the E -F * 28 . 1. angle GHF is equal * to the CD angle GKD : and it was shown that the angle AGK >米 # is equal to the angle GHF ; therefore also 32 ...
Page 34
1. angle ECD is equal t to the interior and opposite angle ABC : but the angle ACE was shown to be equal to the angle BAČ ; therefore the whole +2 Ax . , exterior angle ACD is equal to the two interior and opposite angles CAB , ABC : to ...
1. angle ECD is equal t to the interior and opposite angle ABC : but the angle ACE was shown to be equal to the angle BAČ ; therefore the whole +2 Ax . , exterior angle ACD is equal to the two interior and opposite angles CAB , ABC : to ...
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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 |