The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 40.
Σελίδα 64
... touch a circle , when it meets the circle , and being produced does not cut it . O III . Circles are said to touch one another , which meet , but do not cut one another . IV . Straight lines are said to be equally distant from the ...
... touch a circle , when it meets the circle , and being produced does not cut it . O III . Circles are said to touch one another , which meet , but do not cut one another . IV . Straight lines are said to be equally distant from the ...
Σελίδα 70
Euclides Samuel A Good. Let the two circles ABC , CDE , touch one another internally in the point C ; they have not ... circle ABC , ( I. Def . 15. ) 1. CF is equal to FB ; also , because F is the centre of the circle CDE , 2 . CF is ...
Euclides Samuel A Good. Let the two circles ABC , CDE , touch one another internally in the point C ; they have not ... circle ABC , ( I. Def . 15. ) 1. CF is equal to FB ; also , because F is the centre of the circle CDE , 2 . CF is ...
Σελίδα 74
... circle ABC . Wherefore if a point be taken , & c . Q.E.D. PROP . X. - THEOREM . One circumference of a circle cannot ... touch each other internally , the straight line which joins their centres , being produced , shall pass through the point ...
... circle ABC . Wherefore if a point be taken , & c . Q.E.D. PROP . X. - THEOREM . One circumference of a circle cannot ... touch each other internally , the straight line which joins their centres , being produced , shall pass through the point ...
Σελίδα 75
... circles touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point 4 ; and let F be the centre of the circle ...
... circles touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point 4 ; and let F be the centre of the circle ...
Σελίδα 76
Euclides Samuel A Good. PROP . 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 ...
Euclides Samuel A Good. PROP . 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 ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal adjacent angles AF is equal angle ABC angle ACB angle AGH angle BAC angle BCD angle DEF angle EAB angle EDF angle equal base BC bisected circle ABC cuts the circle describe a circle diameter double equal angles equal Constr equal Hyp equal straight lines equal to BC equiangular equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given rectilineal angle given straight line given triangle gnomon greater inscribed join Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F Q.E.D. PROP rectangle AD rectangle AE rectangle contained rectilineal figure remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC touches the circle triangle ABC triangle DEF twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 26 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 22 - If from the ends of a 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.
Σελίδα 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Σελίδα 97 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - AB; but things which are equal to the same are equal to one another...
Σελίδα 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Σελίδα 53 - IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.
Σελίδα 41 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 52 - 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...