Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ... |
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Σελίδα 116
Of two unequal magnitudes , the greater equals half their sum more half their
difference , the less equals half their sum less half their difference . Given two
magnitudes AB , BC , of which AB is the greater . А , Е ов с And since AC = AB +
BC ...
Of two unequal magnitudes , the greater equals half their sum more half their
difference , the less equals half their sum less half their difference . Given two
magnitudes AB , BC , of which AB is the greater . А , Е ов с And since AC = AB +
BC ...
Σελίδα 117
3 Th . The sum of the sines of any two arcs of a circle , is to the difference of their
sines , as the tangent of half the sum of the arcs is to the tangent of half their
difference . Let AB , AC be two arcs of a circle ABCD ; E its centre ; AEG the
diameter ...
3 Th . The sum of the sines of any two arcs of a circle , is to the difference of their
sines , as the tangent of half the sum of the arcs is to the tangent of half their
difference . Let AB , AC be two arcs of a circle ABCD ; E its centre ; AEG the
diameter ...
Σελίδα 119
A K. E 7 Th . If the base of a triangle be both increased and diminished by the
difference of the two sides ; four rectangles of the sides is to the rectangle of this
sum and difference , as the square of the radius is to the square of the sine of half
...
A K. E 7 Th . If the base of a triangle be both increased and diminished by the
difference of the two sides ; four rectangles of the sides is to the rectangle of this
sum and difference , as the square of the radius is to the square of the sine of half
...
Σελίδα 120
Radius is to the tangent of the excess just mentioned , as the bum is to the
difference of the sides AB , AČ . Produce DA to E ; make AE , AF each equal to
AB ; join BE , and parallel to it draw DG ; through the point F join BG . Then ,
because of ...
Radius is to the tangent of the excess just mentioned , as the bum is to the
difference of the sides AB , AČ . Produce DA to E ; make AE , AF each equal to
AB ; join BE , and parallel to it draw DG ; through the point F join BG . Then ,
because of ...
Σελίδα 125
B KAM B מ 4 Th . A circle being given , two similar polygons may be found , the
one inscribed in the circle , the other described about it , whose difference shall
be less than any given space . Let ABC be the given circle , and LF the square D
...
B KAM B מ 4 Th . A circle being given , two similar polygons may be found , the
one inscribed in the circle , the other described about it , whose difference shall
be less than any given space . Let ABC be the given circle , and LF the square D
...
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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 antecedents applied Argument base bisected centre Chart chord circle circle ABC circumference common consequents Constr contained described diameter difference divided draw drawn equal angles equiangular equilateral equimultiples exceeds excess exterior extreme fore four fourth Geometry given given straight line gles greater half Hence inscribed interior join less magnitudes mean measure meet multiple namely opposite parallel parallelogram pass perpendicular plane polygon produced proportionals propositions proved Q. E. D. Recite radius ratio rectangle rectilineal figure remainders right angles School segment sides similar sine solid square straight line taken tangent third touch triangle ABC unequal Wherefore whole
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
Πληροφορίες βιβλιογραφίας
| Τίτλος | Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ... |
| Συγγραφέας | Dennis M'Curdy |
| Εκδότης | Collins, Brother & Company, 1846 |
| Πρωτότυπο από | Πανεπιστήμιο Χάρβαρντ |
| Ψηφιοποιήθηκε στις | 1 Μαρ. 2007 |
| Μέγεθος | 138 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |