Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ...Collins, Brother & Company, 1846 - 138 sider |
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Resultat 1-5 av 31
Side 7
... Hence , points are by position , central , angular , sectional , or ex- treme . 3. A finite line is that of which the extreme points are given . Note . There are two classes of lines ; namely , straight and curved : of curves there are ...
... Hence , points are by position , central , angular , sectional , or ex- treme . 3. A finite line is that of which the extreme points are given . Note . There are two classes of lines ; namely , straight and curved : of curves there are ...
Side 12
... hence the line BC shall fall on the line EF , and be B equal to it ; otherwise , falling above or below the line EF , two straight lines would enclose a space , which is impossible ( b ) . Therefore , also . the angles at B and C shall ...
... hence the line BC shall fall on the line EF , and be B equal to it ; otherwise , falling above or below the line EF , two straight lines would enclose a space , which is impossible ( b ) . Therefore , also . the angles at B and C shall ...
Side 13
... Hence every equilateral triangle is also equiangular . 6 Th . If two angles ( B , C ) of a triangle ( ABC ) , be equal to one another , the subtending sides ( AC , AB ) of the equal angles shall be equal to one another . Constr . For if ...
... Hence every equilateral triangle is also equiangular . 6 Th . If two angles ( B , C ) of a triangle ( ABC ) , be equal to one another , the subtending sides ( AC , AB ) of the equal angles shall be equal to one another . Constr . For if ...
Side 15
... which was to be done . Recite ( a ) , prop . 3 ; ( d ) , prop . 8 ; ( b ) , prop 1 ; ( e ) , def . 10 . ( c ) , post . 1 ; EB Cor . Hence two straight lines cannot have a common BOOK I. ] 15 SECOND LESSONS IN GEOMETRY .
... which was to be done . Recite ( a ) , prop . 3 ; ( d ) , prop . 8 ; ( b ) , prop 1 ; ( e ) , def . 10 . ( c ) , post . 1 ; EB Cor . Hence two straight lines cannot have a common BOOK I. ] 15 SECOND LESSONS IN GEOMETRY .
Side 16
... Hence two straight lines cannot have a common segment : for if ABC , ABD , have the segment AB common , they cannot both be straight lines . Draw BE at right angles to AB ( a ) then if ABC be a straight line , EBC is a right angle ; and ...
... Hence two straight lines cannot have a common segment : for if ABC , ABD , have the segment AB common , they cannot both be straight lines . Draw BE at right angles to AB ( a ) then if ABC be a straight line , EBC is a right angle ; and ...
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 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
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 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.
Side 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.
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.