The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 236
... angles ; of these the six angles CBA , ACB , ACD , CDA , ADB , DBA are greater than two right angles ; therefore the remaining three angles BAC , CAD , DAB , which contain the solid angle at A , are less than four right angles . Next , let ...
... angles ; of these the six angles CBA , ACB , ACD , CDA , ADB , DBA are greater than two right angles ; therefore the remaining three angles BAC , CAD , DAB , which contain the solid angle at A , are less than four right angles . Next , let ...
Page 237
... solid angle at A , are less than four right angles . Therefore , every solid angle , & c . Q. E. D. PROP . XXII . THEOR . If every two of three plane angles be greater than the third , and if the straight lines which con- tain them be ...
... solid angle at A , are less than four right angles . Therefore , every solid angle , & c . Q. E. D. PROP . XXII . THEOR . If every two of three plane angles be greater than the third , and if the straight lines which con- tain them be ...
Page 238
... angle GHK , the base AL is equal t to the base GK : and because the angles at E , + Hyp . H are greater than the ... solid angle which shall be contained by three given plane angles , any two of them being greater than the third , and ...
... angle GHK , the base AL is equal t to the base GK : and because the angles at E , + Hyp . H are greater than the ... solid angle which shall be contained by three given plane angles , any two of them being greater than the third , and ...
Page 242
... angle ACP . And because ML , LN are equal to AC , CP , each to each , but the angle MLN is greater than * 24 . 1 ... solid angle at R shall be the angle required . Because RX is perpendicular to the plane of the circle LMN , * 3 Def . it ...
... angle ACP . And because ML , LN are equal to AC , CP , each to each , but the angle MLN is greater than * 24 . 1 ... solid angle at R shall be the angle required . Because RX is perpendicular to the plane of the circle LMN , * 3 Def . it ...
Page 243
... angle LRM is equal * * & 1 . to the angle ABC . For the same reason , the angle MRN is equal to the angle DEF , and NRL to GHK . Therefore there is made a solid angle at R , which is contained by three plane angles LRM , MRN , NRL ...
... angle LRM is equal * * & 1 . to the angle ABC . For the same reason , the angle MRN is equal to the angle DEF , and NRL to GHK . Therefore there is made a solid angle at R , which is contained by three plane angles LRM , MRN , NRL ...
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