The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
Euclides. these two is somewhere upon one of those straight lines , and the other upon the other line . Thus the angle ... less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of ... more 2 THE ELEMENTS OF ...
Euclides. these two is somewhere upon one of those straight lines , and the other upon the other line . Thus the angle ... less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of ... more 2 THE ELEMENTS OF ...
Σελίδα 64
... angle bae equal to the angle abd , and produce bd , if necessary , to e ... right angle ; therefore the base ae is equal ( i . 4 ) to the base ec : but ... segment is described . And it is evident that if the angle abd be greater than the ...
... angle bae equal to the angle abd , and produce bd , if necessary , to e ... right angle ; therefore the base ae is equal ( i . 4 ) to the base ec : but ... segment is described . And it is evident that if the angle abd be greater than the ...
Σελίδα 67
... right angle ; but the angle in a seg- ment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle . LET abcd be a circle , of which the diameter is bc , and ...
... right angle ; but the angle in a seg- ment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle . LET abcd be a circle , of which the diameter is bc , and ...
Σελίδα 79
... less than a right angle , each of them being in a segment greater than a semicircle ; but , when the centre is in one of the sides of the triangle , the angle opposite to this side , being in a semicircle , is a right angle ; and , if ...
... less than a right angle , each of them being in a segment greater than a semicircle ; but , when the centre is in one of the sides of the triangle , the angle opposite to this side , being in a semicircle , is a right angle ; and , if ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
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.