Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ...Collins, Brother & Company, 1846 - 138 sider |
Inni boken
Resultat 1-5 av 52
Side 15
... bisect a given rectilineal angle ( BAC ) ; that is , to divide it into two equal angles . Constr . In AB take any ... bisected by the straight line AF ; which was to be done . Recite ( a ) , prop . 3 ; ( b ) , post . 1 ; ( c ) , prop ...
... bisect a given rectilineal angle ( BAC ) ; that is , to divide it into two equal angles . Constr . In AB take any ... bisected by the straight line AF ; which was to be done . Recite ( a ) , prop . 3 ; ( b ) , post . 1 ; ( c ) , prop ...
Side 16
... bisect FG in H ( b ) , and join CF , CH , CG , ( c ) ; CH is perpendicular to AB . D B Argument . The triangles CHF , CHG have CH common , HF equal to HG , and the bases CF , CG are equal radii ; there- fore , the angles CHF , CHG , are ...
... bisect FG in H ( b ) , and join CF , CH , CG , ( c ) ; CH is perpendicular to AB . D B Argument . The triangles CHF , CHG have CH common , HF equal to HG , and the bases CF , CG are equal radii ; there- fore , the angles CHF , CHG , are ...
Side 17
... Bisect AC in E ( a ) ; join BE ( 6 ) and produce it to F ( c ) ; make EF equal to EB ; join FC , and produce AC to G. Argument . The triangles AEB ... bisected , it 2 * BOOK I. ] 17 SECOND LESSONS IN GEOMETRY . 14 Th. If, at a point (B...
... Bisect AC in E ( a ) ; join BE ( 6 ) and produce it to F ( c ) ; make EF equal to EB ; join FC , and produce AC to G. Argument . The triangles AEB ... bisected , it 2 * BOOK I. ] 17 SECOND LESSONS IN GEOMETRY . 14 Th. If, at a point (B...
Side 18
... bisected , it may be proved that the angle BCG , or its equal ACD , is greater than the angle ABC . Therefore , if one side of a triangle , & c . Q. E. D. Recite ( a ) , p . 10 ; ( c ) , pos . 2 ; ( b ) , pos . 1 ; ( d ) , p . 4 , 15 ...
... bisected , it may be proved that the angle BCG , or its equal ACD , is greater than the angle ABC . Therefore , if one side of a triangle , & c . Q. E. D. Recite ( a ) , p . 10 ; ( c ) , pos . 2 ; ( b ) , pos . 1 ; ( d ) , p . 4 , 15 ...
Side 25
... bisected by BC . Wherefore , the opposite Recite ( a ) , p . 9 , 10 ; ( d ) , p . 27 ; sides and angles , & c ... bisect AF , and also each of the parallelograms ; and the triangle DBC will be the half of each ( b ) ; hence the parallelo ...
... bisected by BC . Wherefore , the opposite Recite ( a ) , p . 9 , 10 ; ( d ) , p . 27 ; sides and angles , & c ... bisect AF , and also each of the parallelograms ; and the triangle DBC will be the half of each ( b ) ; hence the parallelo ...
Andre utgaver - Vis alle
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... Dennis M'Curdy Uten tilgangsbegrensning - 1846 |
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Ingen forhåndsvisning tilgjengelig - 2017 |
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 26 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Side 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.
Side 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.
Side 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...
Side 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