The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
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Αποτελέσματα 6 - 10 από τα 20.
Σελίδα 60
... angle , is greater than the squares of the sides containing the obtuse angle ... B C D Because the straight line BD is divided into two parts in the point C ... angle at D is a right angle ; and the square of CA is equal ( I. 47. ) to the ...
... angle , is greater than the squares of the sides containing the obtuse angle ... B C D Because the straight line BD is divided into two parts in the point C ... angle at D is a right angle ; and the square of CA is equal ( I. 47. ) to the ...
Σελίδα 81
... BCD . A D G C E4 F B Because E is the centre of the circles BCD , AFG ; ( I. Def . 15. ) 1. EA is equal to EF , and ED to EB ; therefore the two sides AE , EB , are equal to the two FE , ED , each to each ; and they contain the angle at ...
... BCD . A D G C E4 F B Because E is the centre of the circles BCD , AFG ; ( I. Def . 15. ) 1. EA is equal to EF , and ED to EB ; therefore the two sides AE , EB , are equal to the two FE , ED , each to each ; and they contain the angle at ...
Σελίδα 84
... angle BFD is at the centre , and the angle BAD at the circumference , and that they have the same part of the circumference , viz . BCD for their base ; therefore ( III . 20. ) 1. The angle BFD is double of the angle BAD : for the same ...
... angle BFD is at the centre , and the angle BAD at the circumference , and that they have the same part of the circumference , viz . BCD for their base ; therefore ( III . 20. ) 1. The angle BFD is double of the angle BAD : for the same ...
Σελίδα 86
... BCD , and join CA , DA . And because the segment ACB is similar ( Hyp . ) to the segment ADB , and that similar segments of circles contain` ( IÏÏ . Def . 11. ) equal angles ; 2. The angle ACB is equal to the angle ADB , the exterior to ...
... BCD , and join CA , DA . And because the segment ACB is similar ( Hyp . ) to the segment ADB , and that similar segments of circles contain` ( IÏÏ . Def . 11. ) equal angles ; 2. The angle ACB is equal to the angle ADB , the exterior to ...
Σελίδα 91
... angle ACD is equal to the angle BCD , because each of them is a right angle ; therefore ( I. 4. ) 3. The base AD is equal to the basė BD . But equal straight lines cut off ( III . 28. ) equal circumferences , the greater equal to the ...
... angle ACD is equal to the angle BCD , because each of them is a right angle ; therefore ( I. 4. ) 3. The base AD is equal to the basė BD . But equal straight lines cut off ( III . 28. ) equal circumferences , the greater equal to the ...
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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...