The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 3
... less than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . A figure is that which is inclosed by one or more boundaries . XV . A circle is a plane figure contained by one line , which is called the ...
... less than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . A figure is that which is inclosed by one or more boundaries . XV . A circle is a plane figure contained by one line , which is called the ...
Page 7
... less than " two right angles , these straight lines being continually produced , shall at length meet upon that side on which are the angles " which are less than two right angles . " See the notes on Prop . xxix . of Book 1. Oct. Ed ...
... less than " two right angles , these straight lines being continually produced , shall at length meet upon that side on which are the angles " which are less than two right angles . " See the notes on Prop . xxix . of Book 1. Oct. Ed ...
Page 9
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is re- quired to cut off from AB , the greater , a part equal to C , the less . From the point A draw * the E B * 2.1 . straight line AD equal to C ...
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is re- quired to cut off from AB , the greater , a part equal to C , the less . From the point A draw * the E B * 2.1 . straight line AD equal to C ...
Page 11
... less , and * 3.1 . join FC , GB . Hyp . A * 4.1 . Because AF is equal to + AG , and AB tot AC , Const . the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two trian- gles AFC ...
... less , and * 3.1 . join FC , GB . Hyp . A * 4.1 . Because AF is equal to + AG , and AB tot AC , Const . the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two trian- gles AFC ...
Page 13
... less to the greater , which is absurd . There- fore AB is not unequal to AC , that is , it is equal to it . Where- fore , if two angles , & c . Q. E. D. B DA COR . Hence every equiangular triangle is also equilateral . PROP . VII ...
... less to the greater , which is absurd . There- fore AB is not unequal to AC , that is , it is equal to it . Where- fore , if two angles , & c . Q. E. D. B DA COR . Hence every equiangular triangle is also equilateral . PROP . VII ...
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