The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Seite 6
... bac equal to the angle e df , the base bc shall be equal to the base ef ; and the triangle abc to the triangle def ... angle a cb to dfe . Therefore , if two triangles have two sides of the one equal to two sides of the other , each to ...
... bac equal to the angle e df , the base bc shall be equal to the base ef ; and the triangle abc to the triangle def ... angle a cb to dfe . Therefore , if two triangles have two sides of the one equal to two sides of the other , each to ...
Seite 9
... angle bac coincides with the angle ed f , and is equal ( Sax . ) to it . Therefore if two triangles , & c . Q.E.D. PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac ...
... angle bac coincides with the angle ed f , and is equal ( Sax . ) to it . Therefore if two triangles , & c . Q.E.D. PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac ...
Seite 13
Euclides. are equal to the angles aed , deb . Take away the common angle a e d , and the remaining angle ce a is ... bac . Bisect ( i . 10 ) a c in e , join be and produce it to f , and make e f equal to be ; join also fc , and produce ...
Euclides. are equal to the angles aed , deb . Take away the common angle a e d , and the remaining angle ce a is ... bac . Bisect ( i . 10 ) a c in e , join be and produce it to f , and make e f equal to be ; join also fc , and produce ...
Seite 14
... bac , acb , as also cab , abc , are less than two right angles . There- fore any two angles , & c . Q. E. D. b PROPOSITION XVIII . - THEOREM . The greater side of every triangle is opposite to the greater angle . d с LET abc be a ...
... bac , acb , as also cab , abc , are less than two right angles . There- fore any two angles , & c . Q. E. D. b PROPOSITION XVIII . - THEOREM . The greater side of every triangle is opposite to the greater angle . d с LET abc be a ...
Seite 15
... angle bed of the triangle dcb is greater than its angle bdc , and that the greater ( i . 19 ) side is posite to the ... bac a e a ro Produce bd to e ; and because two sides of a triangle are greater than the third side , the two sides ba ...
... angle bed of the triangle dcb is greater than its angle bdc , and that the greater ( i . 19 ) side is posite to the ... bac a e a ro Produce bd to e ; and because two sides of a triangle are greater than the third side , the two sides ba ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc 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 ILLUSTRATED LONDON 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 straight line drawn tiple touches the circle triangle abc triangle def twice the rectangle
Beliebte Passagen
Seite 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.
Seite 42 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Seite 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 21 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Seite 29 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 38 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Seite 15 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Seite 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 4 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 126 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.