The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 2
A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter .
A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter .
Σελίδα 24
The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . A parallelogram is a four - sided figure , of which the opposite sides are parallel ...
The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . A parallelogram is a four - sided figure , of which the opposite sides are parallel ...
Σελίδα 26
35 ) to dbcf , because they are upon the same base bc , and between the same parallels bc , ef ; and the triangle abc is the half of the parallelogram ebca , because the diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the ...
35 ) to dbcf , because they are upon the same base bc , and between the same parallels bc , ef ; and the triangle abc is the half of the parallelogram ebca , because the diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the ...
Σελίδα 28
34 ) of the triangle a b c , because the diameter ac divides it into two equal parts ; wherefore a b c d b is also double of the triangle e bc . Therefore , if a parallelogram , & c . Q. E. D. PROPOSITION XLII . PROBLEM .
34 ) of the triangle a b c , because the diameter ac divides it into two equal parts ; wherefore a b c d b is also double of the triangle e bc . Therefore , if a parallelogram , & c . Q. E. D. PROPOSITION XLII . PROBLEM .
Σελίδα 29
THEOREM . a The complements of the parallelograms , which are about the diameter of any parallelogram , are equal to one another . LET abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pah d rallelograms about ...
THEOREM . a The complements of the parallelograms , which are about the diameter of any parallelogram , are equal to one another . LET abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pah d rallelograms about ...
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abcd angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given rectilineal given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 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...
Σελίδα 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.