The first six books of the Elements of Euclid, with numerous exercises |
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Seite 50
If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and if it cuts it at right angles , it shall bisect it .
If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and if it cuts it at right angles , it shall bisect it .
Seite 51
Again , because the straight line fe bisects the straight line bd , which does not pass through the centre , it shall cut it at right angles ( iii . 3 ) : wherefore feb is a right angle : and fea was shewn to be a right angle ...
Again , because the straight line fe bisects the straight line bd , which does not pass through the centre , it shall cut it at right angles ( iii . 3 ) : wherefore feb is a right angle : and fea was shewn to be a right angle ...
Seite 55
The straight line which joins the centres f , g , being produced , passes through the point a For , if not ... line which joins the points f , g cannot fall other¬ wise than upon the point a , that is , it must pass through it .
The straight line which joins the centres f , g , being produced , passes through the point a For , if not ... line which joins the points f , g cannot fall other¬ wise than upon the point a , that is , it must pass through it .
Seite 56
Therefore gh passes through the point of contact ( iii . 11 ) ; but it does not pass through it , because the points b , d are without the straight line which is absurd . Therefore one circle cannot touch another on the in- side in more ...
Therefore gh passes through the point of contact ( iii . 11 ) ; but it does not pass through it , because the points b , d are without the straight line which is absurd . Therefore one circle cannot touch another on the in- side in more ...
Seite 57
Then , because the straight line ef , passing through the centre , cuts the straight line ab , which does not pass through the centre , at right angles , it also bisects it ( iii . 3 ) ; wherefore a f is equal to fb , and ab double of ...
Then , because the straight line ef , passing through the centre , cuts the straight line ab , which does not pass through the centre , at right angles , it also bisects it ( iii . 3 ) ; wherefore a f is equal to fb , and ab double of ...
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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.