The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Seite 45
... centre at g the distance gb or gf , de- scribe the semicircle bhf , and produce de to h , and join gh : therefore because the straight line bf is divided into two equal parts in the point g , and into two unequal b مع g с e rd at e ...
... centre at g the distance gb or gf , de- scribe the semicircle bhf , and produce de to h , and join gh : therefore because the straight line bf is divided into two equal parts in the point g , and into two unequal b مع g с e rd at e ...
Seite 47
... centre of a circle , when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls is said to be farther from the centre . Definitions IV . and V. VI . A segment of a ...
... centre of a circle , when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls is said to be farther from the centre . Definitions IV . and V. VI . A segment of a ...
Seite 48
... centre , and the circumference between them . Definition X. XI . Similar segments of a circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a ...
... centre , and the circumference between them . Definition X. XI . Similar segments of a circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a ...
Seite 49
... centre g * : therefore the angle a dg is equal ( i . 8 ) to the angle gdb . But when a straight line standing upon ... centre of the circle a b c In the same manner it can be shewn , that no other point but fis the centre ; that is , f ...
... centre g * : therefore the angle a dg is equal ( i . 8 ) to the angle gdb . But when a straight line standing upon ... centre of the circle a b c In the same manner it can be shewn , that no other point but fis the centre ; that is , f ...
Seite 50
... centre , bisect any straight line a b , which does not pass through the centre , in the point f ; it cuts it also at right angles . Take ( i . 3 ) e the centre of the circle , and join e a , e b . Then , because af is equal to fb , and ...
... centre , bisect any straight line a b , which does not pass through the centre , in the point f ; it cuts it also at right angles . Take ( i . 3 ) e the centre of the circle , and join e a , e b . Then , because af is equal to fb , and ...
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Häufige Begriffe und Wortgruppen
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
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.