The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 sider |
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Resultater 1-5 af 34
Side 6
... angle 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 ; and the other angles to which the equal sides are opposite , shall be equal , each to each , viz . the angle abc ...
... angle 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 ; and the other angles to which the equal sides are opposite , shall be equal , each to each , viz . the angle abc ...
Side 9
... angle bac coincides with the angle ed f , and is equal ( 8ax . ) 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 ( 8ax . ) 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 ...
Side 13
Euclides. are equal to the angles aed , deb . Take away the common angle a e d , and the remaining angle cea is equal ... 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 cea is equal ... 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 ...
Side 14
... bac , acb , as also cab , abc , are less than two right angles . fore any two angles , & c . Q. E. D. PROPOSITION XVIII . - THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of ...
... bac , acb , as also cab , abc , are less than two right angles . fore any two angles , & c . Q. E. D. PROPOSITION XVIII . - THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of ...
Side 15
Euclides. a d bcd is greater than the angle adc ; and because the angle bcd ... bac . e Produce bd to e ; and because two sides of a triangle are greater ... angle of a triangle is greater than the interior and opposite angle , the ...
Euclides. a d bcd is greater than the angle adc ; and because the angle bcd ... bac . e Produce bd to e ; and because two sides of a triangle are greater ... angle of a triangle is greater than the interior and opposite angle , the ...
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Almindelige termer og sætninger
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 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 pentagon perpendicular Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment shewn square of a c square of eg straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle
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Side 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.
Side 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.
Side 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 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...
Side 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...
Side 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 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...
Side 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.