Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ...Collins, Brother & Company, 1846 - 138 páginas |
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Página 7
... pass through the same point . 5. A circular line is the path of a moving point about a stationary one , at the same uniform distance from it . 6. A superficies is the upper or outside face - the surface : it has two dimensions - length ...
... pass through the same point . 5. A circular line is the path of a moving point about a stationary one , at the same uniform distance from it . 6. A superficies is the upper or outside face - the surface : it has two dimensions - length ...
Página 28
... passes , are EH , GF ; and the complements , which make up the whole figure , are E JK BK , KD , which are said to be equal . The diameter AC bisects the parallelogram ABCD ; its parts AK , KC bisect also EH , GF ( a ) ; there- fore ...
... passes , are EH , GF ; and the complements , which make up the whole figure , are E JK BK , KD , which are said to be equal . The diameter AC bisects the parallelogram ABCD ; its parts AK , KC bisect also EH , GF ( a ) ; there- fore ...
Página 41
... ; ( e ) p . 4 , 1 ; ( c ) post . 1 ; ( f ) def . 15 , 1 . Corollary . The line which bisects another at right angles in a circle , passes through the centre of a circle . 2 Th . If any two points ( A , BOOK THIRD. ...
... ; ( e ) p . 4 , 1 ; ( c ) post . 1 ; ( f ) def . 15 , 1 . Corollary . The line which bisects another at right angles in a circle , passes through the centre of a circle . 2 Th . If any two points ( A , BOOK THIRD. ...
Página 42
... pass through the centre , they do not bisect each other . Argument 1. Let F be the centre ; then , if AC pass through it , BD cannot pass through F , by hyp .; therefore AC is not bisected by BD ( a ) . 2. If neither of the chords pass ...
... pass through the centre , they do not bisect each other . Argument 1. Let F be the centre ; then , if AC pass through it , BD cannot pass through F , by hyp .; therefore AC is not bisected by BD ( a ) . 2. If neither of the chords pass ...
Página 43
... passes through the centre ( E ) : and FD , the other part of the diameter , is the least : and other lines drawn from that point diminish as they recede from the greatest towards the least : also from the same point , only two equal ...
... passes through the centre ( E ) : and FD , the other part of the diameter , is the least : and other lines drawn from that point diminish as they recede from the greatest towards the least : also from the same point , only two equal ...
Otras ediciones - Ver todas
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Sin vista previa disponible - 2017 |
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Sin vista previa disponible - 2017 |
Términos y frases comunes
ABCD alternate angles angle ACD angles ABC angles equal antecedents Argument base BC bisected centre Chart chord circle ABC circumference Constr Denison Olmsted diameter draw drawn equal angles equal arcs equal radii equal sides equals the squares equi equiangular equilateral equilateral polygon equimultiples exterior angle fore Geometry given circle given rectilineal given straight line gles gnomon greater half inscribed isosceles isosceles triangle join less meet multiple opposite angles parallelogram parallelopipeds pentagon perimeter perpendicular plane polygon produced propositions Q. E. D. Recite radius ratio rectangle rectilineal figure School segment semicircle similar similar triangles sine square of AC tangent touches the circle triangle ABC unequal Wherefore
Pasajes populares
Página 90 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Página 117 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Página 92 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Página 79 - THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the sixth.
Página 87 - If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally...
Página 26 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Página 94 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Página 12 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Página 133 - If a straight line stand at right angles to each of two straight lines at the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are.
Página 13 - AB be the greater, and from it cut (3. 1.) off DB equal to AC the less, and join DC ; therefore, because A in the triangles DBC, ACB, DB is equal to AC, and BC common to both, the two sides DB, BC are equal to the two AC, CB. each to each ; and the angle DBC is equal to the angle ACB; therefore the base DC is equal to the base AB, and the triangle DBC is< equal to the triangle (4. 1.) ACB, the less to 'the greater; which is absurd.