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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Side 5
... ratio , and a slight alteration in the method of compounding ra- tios . Nevertheless , care has been taken to introduce nothing which could not be directly employed in drawing out the properties of proportionals according to the rigor ...
... ratio , and a slight alteration in the method of compounding ra- tios . Nevertheless , care has been taken to introduce nothing which could not be directly employed in drawing out the properties of proportionals according to the rigor ...
Side 60
... ratio to each other . 2. One rectilineal figure is described about another , when all the sides of the former pass through the angular points of the latter . 3. A rectilineal figure is inscribed in a circle , when the angles of the ...
... ratio to each other . 2. One rectilineal figure is described about another , when all the sides of the former pass through the angular points of the latter . 3. A rectilineal figure is inscribed in a circle , when the angles of the ...
Side 69
... Ratio is the numerical relation of antecedent and consequent , or the number of times , or parts of times , which the latter contains the former . Or , Ratio is the numerical relation of measure and magnitude , or the number of times ...
... Ratio is the numerical relation of antecedent and consequent , or the number of times , or parts of times , which the latter contains the former . Or , Ratio is the numerical relation of measure and magnitude , or the number of times ...
Side 70
... ratio of the first to the fourth is the triplicate or cube of the ratio of the first to the second . Such ratios are called compound . 10. And when any number of magnitudes of the same kind are in a certain order , however different the ...
... ratio of the first to the fourth is the triplicate or cube of the ratio of the first to the second . Such ratios are called compound . 10. And when any number of magnitudes of the same kind are in a certain order , however different the ...
Side 72
... ratio to the second which the third has to the fourth ; then any equimultiples of the antecedents shall have the same ratio as any equimultiples of the consequents . Let A , B , C , D , be four magni- tudes ; such that A is to B as C is ...
... ratio to the second which the third has to the fourth ; then any equimultiples of the antecedents shall have the same ratio as any equimultiples of the consequents . Let A , B , C , D , be four magni- tudes ; such that A is to B as C is ...
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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