The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Page 456
... radius of the circle of which the measure of a given angle is an arch , that arch will contain the same number of degrees , minutes , se- conds , & c . as is manifest from Lemma 2 . III . Let AB be produced till it meet the circle again ...
... radius of the circle of which the measure of a given angle is an arch , that arch will contain the same number of degrees , minutes , se- conds , & c . as is manifest from Lemma 2 . III . Let AB be produced till it meet the circle again ...
Page 457
... radius CB to the radius NB , and AE to MP as AB to BM and BC or BA to BD , as BN or BM to BO ; ) and by conversion , DA to MO as AB to MB . Hence the corollary is manifest : there- fore , if the radius be supposed to be divided into any ...
... radius CB to the radius NB , and AE to MP as AB to BM and BC or BA to BD , as BN or BM to BO ; ) and by conversion , DA to MO as AB to MB . Hence the corollary is manifest : there- fore , if the radius be supposed to be divided into any ...
Page 458
... radius is a mean proportional between the cosine and secant of any angle ABC . Since CD , AE , are parallel , BD is to BC or BA as BA to BE . PROP . I. FIG . 5 . In a right angled plane triangle ; if the hypothenuse be made radius , the ...
... radius is a mean proportional between the cosine and secant of any angle ABC . Since CD , AE , are parallel , BD is to BC or BA as BA to BE . PROP . I. FIG . 5 . In a right angled plane triangle ; if the hypothenuse be made radius , the ...
Page 459
... radius , the sides are the sines of the angles opposite to them , and the radius is the sine of a right angle ( cor . to def . 4. ) which is opposite to the hypothenuse . In any oblique angled triangle ABC , any two sides AB , AC , will ...
... radius , the sides are the sines of the angles opposite to them , and the radius is the sine of a right angle ( cor . to def . 4. ) which is opposite to the hypothenuse . In any oblique angled triangle ABC , any two sides AB , AC , will ...
Page 460
... radius , BE , BG , are the tan- gents of the angles EFB , BFG ; but it is manifest that EC is the sum of the sides ... radius is to the tan- gent of an angle ; and the radius is to the tangent of the excess of this angle above half a ...
... radius , BE , BG , are the tan- gents of the angles EFB , BFG ; but it is manifest that EC is the sum of the sides ... radius is to the tan- gent of an angle ; and the radius is to the tangent of the excess of this angle above half a ...
Other editions - View all
The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore