The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that which is enclosed by one or more boundaries . XV . A circle is a plain figure contained by one line , which is ...
... less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that which is enclosed by one or more boundaries . XV . A circle is a plain figure contained by one line , which is ...
Σελίδα 4
... 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 describe an equilateral ...
... 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 describe an equilateral ...
Σελίδα 5
... less , LET ab and c be the two given straight lines , whereof a b is the greater . It is required to cut off from a b , the greater , a part equal to c , the less . From the point a draw ( i . 2 ) the straight line a d equal to c ; and ...
... less , LET ab and c be the two given straight lines , whereof a b is the greater . It is required to cut off from a b , the greater , a part equal to c , the less . From the point a draw ( i . 2 ) the straight line a d equal to c ; and ...
Σελίδα 6
... less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two 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 ...
... less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two 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 ...
Σελίδα 7
... less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the two 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 ...
... less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the two 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 ...
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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