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
... touch and do not cut one another ; one line insists upon another when it stands upon a point in the other : one line is parallel to another when it is in the same plane with the other , and at all points equidistant from it : lines ...
... touch and do not cut one another ; one line insists upon another when it stands upon a point in the other : one line is parallel to another when it is in the same plane with the other , and at all points equidistant from it : lines ...
Página 41
... touching a circle , without cutting it , however produced . 3. A circle touches a circle when they meet and do not cut one another . 4. Chords are equidistant from the centre , when the perpendiculars drawn to them from the centre are ...
... touching a circle , without cutting it , however produced . 3. A circle touches a circle when they meet and do not cut one another . 4. Chords are equidistant from the centre , when the perpendiculars drawn to them from the centre are ...
Página 43
... touch each other internally , they shall not have the same centre . Argument . For , if possible , let F be the com- mon centre , and C the point of contact : join FC , and draw a straight line FEB to meet the circles in E and B. Then ...
... touch each other internally , they shall not have the same centre . Argument . For , if possible , let F be the com- mon centre , and C the point of contact : join FC , and draw a straight line FEB to meet the circles in E and B. Then ...
Página 46
... touch one another internally ( in A ) , the straight line which joins their cen- tres , being produced , shall pass through their point of con- tact . Argument . Let F , G , be their central points : then , if GF which joins them do not ...
... touch one another internally ( in A ) , the straight line which joins their cen- tres , being produced , shall pass through their point of con- tact . Argument . Let F , G , be their central points : then , if GF which joins them do not ...
Página 47
... touch another on the inside in more than one point . 2. Again , let the circles ABC , ACK touch each other externally , as in A , C ; join AC . Then because the points A , C , are in the circumference of each of the circles , the chord ...
... touch another on the inside in more than one point . 2. Again , let the circles ABC , ACK touch each other externally , as in A , C ; join AC . Then because the points A , C , are in the circumference of each of the circles , the chord ...
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 Q. E. D. Recite radius ratio rectangle rectangle contained 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 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.
Página 71 - If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; then shall...
Página 83 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words