The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 3
... sides . XXV . An isosceles triangle is that which has only two sides equal . Δ Δ Δ Equilateral . Isosceles . Scalene . XXVI . A scalene triangle is that which has three unequal sides . XXVII . A right - angled triangle is that which has ...
... sides . XXV . An isosceles triangle is that which has only two sides equal . Δ Δ Δ Equilateral . Isosceles . Scalene . XXVI . A scalene triangle is that which has three unequal sides . XXVII . A right - angled triangle is that which has ...
Σελίδα 4
... side of it taken together 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 . PROPOSITION I. — PROBLEM . To ...
... side of it taken together 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 . PROPOSITION I. — PROBLEM . To ...
Σελίδα 6
... sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall ...
... sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall ...
Σελίδα 7
... sides fa , a c are equal to the two ga , ab , each to each ; and they contain the angle fag common to the two triangles a fc , agb ; there- fore the base fc is equal ( i . 4 ) to the base gb , and the triangle afc to the triangle a gb ...
... sides fa , a c are equal to the two ga , ab , each to each ; and they contain the angle fag common to the two triangles a fc , agb ; there- fore the base fc is equal ( i . 4 ) to the base gb , and the triangle afc to the triangle a gb ...
Σελίδα 8
... side of it , which have their sides ca , da terminated in the extremity a of the base equal to one another , and like- wise their sides cb , db , that are terminated in b . a bcd ; much greater Again , because cb is angle bcd ; but it ...
... side of it , which have their sides ca , da terminated in the extremity a of the base equal to one another , and like- wise their sides cb , db , that are terminated in b . a bcd ; much greater Again , because cb is angle bcd ; but it ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle