Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ...Collins, Brother & Company, 1846 - 138 σελίδες |
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Αποτελέσματα 1 - 5 από τα 31.
Σελίδα 34
... similar reasons , HF is a square on HG , which is equal to AC . It is also plain that AG is the rectangle of AC and CG , or CB ; also , that GE is the rectangle of GF and GK , which are equal to AC and CB . Now the two squares and two ...
... similar reasons , HF is a square on HG , which is equal to AC . It is also plain that AG is the rectangle of AC and CG , or CB ; also , that GE is the rectangle of GF and GK , which are equal to AC and CB . Now the two squares and two ...
Σελίδα 41
... Similar segments of a circle are those which contain equal angles . DD Propositions . 1 P. To find the centre of a given circle ( ABC ) . Construction . In the circle draw any chord AB , and bisect it in D ( a ) ; through D draw CE at ...
... Similar segments of a circle are those which contain equal angles . DD Propositions . 1 P. To find the centre of a given circle ( ABC ) . Construction . In the circle draw any chord AB , and bisect it in D ( a ) ; through D draw CE at ...
Σελίδα 51
... similar segments of circles can be described , which shall not coincide with each other . If possible , let the segments ACB , ADB , which are on the same side of AB , and do not coincide , be similar . Then , since the circles , of ...
... similar segments of circles can be described , which shall not coincide with each other . If possible , let the segments ACB , ADB , which are on the same side of AB , and do not coincide , be similar . Then , since the circles , of ...
Σελίδα 52
... Similar segments of circles ( AEB , CFD ) , upon equal chords ( AB , CD ) , are equal to each other . Argument . If ... similar ( b ) : therefore , the perimeters every- where coincide and bound the same space ( c ) . Therefore , similar ...
... Similar segments of circles ( AEB , CFD ) , upon equal chords ( AB , CD ) , are equal to each other . Argument . If ... similar ( b ) : therefore , the perimeters every- where coincide and bound the same space ( c ) . Therefore , similar ...
Σελίδα 85
... greater than the other , the difference is a multiple of the same measuring unit . Therefore , if the same unit , & c . Q. E. D. BOOK SIXTH . Definitions . 1. Similar rectilineal figures are BOOK V. ] 85 SECOND LESSONS IN GEOMETRY .
... greater than the other , the difference is a multiple of the same measuring unit . Therefore , if the same unit , & c . Q. E. D. BOOK SIXTH . Definitions . 1. Similar rectilineal figures are BOOK V. ] 85 SECOND LESSONS IN GEOMETRY .
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 26 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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