The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 3
... besides these are called trape- ziums . XXXV . Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS .
... besides these are called trape- ziums . XXXV . Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS .
Página 19
... parallel . LET the straight line ef , which falls upon the two straight lines ab , cd , make the alternate angles aef , efd equal to one another ; a b is parallel to cd . For , if it be not parallel , a b BOOK I. PROP . XXVII . 19.
... parallel . LET the straight line ef , which falls upon the two straight lines ab , cd , make the alternate angles aef , efd equal to one another ; a b is parallel to cd . For , if it be not parallel , a b BOOK I. PROP . XXVII . 19.
Página 20
... parallel ( 35 def . ) to one another . ab there- fore is parallel to cd . Wherefore , if a straight line , & c . Q. E. D. PROPOSITION XXVIII . - THEOREM . If a straight line falling upon two other straight lines makes the exterior angle ...
... parallel ( 35 def . ) to one another . ab there- fore is parallel to cd . Wherefore , if a straight line , & c . Q. E. D. PROPOSITION XXVIII . - THEOREM . If a straight line falling upon two other straight lines makes the exterior angle ...
Página 21
... parallel straight lines ab , cd ; the alternate angles agh , ghd , are equal to one another ; and the exterior angle egb is equal to the interior and opposite , upon the same side ghd ; and the two interior angles bg h , ghd upon the ...
... parallel straight lines ab , cd ; the alternate angles agh , ghd , are equal to one another ; and the exterior angle egb is equal to the interior and opposite , upon the same side ghd ; and the two interior angles bg h , ghd upon the ...
Página 22
... parallel ( i . 27 ) to be . Therefore the straight line e af is drawn through the given point a parallel to the given straight line b c . Which was to be done . PROPOSITION XXXII . - THEOREM . If a side of any triangle be produced , the ...
... parallel ( i . 27 ) to be . Therefore the straight line e af is drawn through the given point a parallel to the given straight line b c . Which was to be done . PROPOSITION XXXII . - THEOREM . If a side of any triangle be produced , the ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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.
Página 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...
Página 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...
Página 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 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...
Página 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.