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 11 - 15 από τα 35.
Σελίδα 67
... manner it may be demonstrated that it does not fall upon the circumference ; therefore 7. AB falls within the circle . Wherefore , if any two points , & c . , Q.E.D. PROP . III . - THEOREM . If a straight line drawn through the centre ...
... manner it may be demonstrated that it does not fall upon the circumference ; therefore 7. AB falls within the circle . Wherefore , if any two points , & c . , Q.E.D. PROP . III . - THEOREM . If a straight line drawn through the centre ...
Σελίδα 72
... manner it may be shown that 4. FD is greater than CD : therefore DA is the greatest , and DE greater than DF , and DF than DC . And because MK , KD , are greater ( I. 20. ) than MD , and MK is equal ( I. Def . 15. ) to MG , the ...
... manner it may be shown that 4. FD is greater than CD : therefore DA is the greatest , and DE greater than DF , and DF than DC . And because MK , KD , are greater ( I. 20. ) than MD , and MK is equal ( I. Def . 15. ) to MG , the ...
Σελίδα 73
Euclides Samuel A Good. In like manner it may be shown , that 4. DL is less than DH : therefore DG is the least , and DK less than DL , and DL than DH . Also , there can be drawn only two equal straight ... manner it may be shown, that ...
Euclides Samuel A Good. In like manner it may be shown , that 4. DL is less than DH : therefore DG is the least , and DK less than DL , and DL than DH . Also , there can be drawn only two equal straight ... manner it may be shown, that ...
Σελίδα 74
Euclides Samuel A Good. In like manner it may be demonstrated that no other point but D is the centre ; therefore 3. D is the centre of the circle ABC . Wherefore if a point be taken , & c . Q.E.D. PROP . X. - THEOREM . One circumference ...
Euclides Samuel A Good. In like manner it may be demonstrated that no other point but D is the centre ; therefore 3. D is the centre of the circle ABC . Wherefore if a point be taken , & c . Q.E.D. PROP . X. - THEOREM . One circumference ...
Σελίδα 80
... manner it may be demonstrated that it does not fall upon the circumference ; therefore . 4. The straight line drawn from A at right angles to BA must fall without the circle , as AE . And between the straight line AE and the ...
... manner it may be demonstrated that it does not fall upon the circumference ; therefore . 4. The straight line drawn from A at right angles to BA must fall without the circle , as AE . And between the straight line AE and 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...