The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Αποτελέσματα 1 - 5 από τα 26.
Σελίδα 47
... circles be applied to one another , so that their centres coincide , the circles must likewise coincide , since the straight lines from the centres are equal . II . A straight line is said to touch a circle when it meets the circle ...
... circles be applied to one another , so that their centres coincide , the circles must likewise coincide , since the straight lines from the centres are equal . II . A straight line is said to touch a circle when it meets the circle ...
Σελίδα 51
... circle , & c . Q. E. D. PROPOSITION V. — THEOREM . If two circles cut one another , they shall not have the same ... touch one another internally , they shall not have the same centre . LET the two circles abc , cde , touch one another ...
... circle , & c . Q. E. D. PROPOSITION V. — THEOREM . If two circles cut one another , they shall not have the same ... touch one another internally , they shall not have the same centre . LET the two circles abc , cde , touch one another ...
Σελίδα 54
... circle . LET the point d be taken within the circle abc , from which to the cir- cumference there fall more than two equal straight lines , viz . da , db , dc , the point d is the centre of the ... circles touch 54 THE ELEMENTS OF EUCLID .
... circle . LET the point d be taken within the circle abc , from which to the cir- cumference there fall more than two equal straight lines , viz . da , db , dc , the point d is the centre of the ... circles touch 54 THE ELEMENTS OF EUCLID .
Σελίδα 55
Euclides. PROPOSITION XI . - THEOREM . If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact ... circle cannot touch BOOK III . PROPS . XI . , XII . 55.
Euclides. PROPOSITION XI . - THEOREM . If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact ... circle cannot touch BOOK III . PROPS . XI . , XII . 55.
Σελίδα 56
Euclides. PROPOSITION XIII . - THEOREM . One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle ebf touch the circle abc in more points than one ...
Euclides. PROPOSITION XIII . - THEOREM . One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle ebf touch the circle abc in more points than one ...
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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 perpendicular Q. E. D. PROPOSITION rectangle a b 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 40 - 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 2 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 19 - 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 27 - 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 36 - 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 13 - 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 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 2 - 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 124 - 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.