Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ... |
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Σελίδα 69
The first of four magnitudes has the same ratio to the second which the third has
to the fourth , when equimultiples of the first and third , also of the second and
fourth , being taken ; if the multiple of the first be greater than that of the second ,
the ...
The first of four magnitudes has the same ratio to the second which the third has
to the fourth , when equimultiples of the first and third , also of the second and
fourth , being taken ; if the multiple of the first be greater than that of the second ,
the ...
Σελίδα 70
the second is the consequent of the first , the third that of the second , and the
fourth that of the third ; then 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 .
the second is the consequent of the first , the third that of the second , and the
fourth that of the third ; then 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 .
Σελίδα 72
... the fourth ; and if of the first and third equimultiples be taken , these shall be
equimultiples , one of the second the other ... and if EF be taken the second
multiple of A , and GH the second multiple of C : then will EF be the fourth mul - kt
tiple of ...
... the fourth ; and if of the first and third equimultiples be taken , these shall be
equimultiples , one of the second the other ... and if EF be taken the second
multiple of A , and GH the second multiple of C : then will EF be the fourth mul - kt
tiple of ...
Σελίδα 74
D D A Th . If the first of four magnitudes have to the second the same ratio which
the third has to the fourth ; then , if the first be greater than the second , the third is
also greater than the fourth ; if equal , equal ; and if less , less . Let equimultiples
...
D D A Th . If the first of four magnitudes have to the second the same ratio which
the third has to the fourth ; then , if the first be greater than the second , the third is
also greater than the fourth ; if equal , equal ; and if less , less . Let equimultiples
...
Σελίδα 81
B D E F A 18 Th . If the first be to the second as the third is to the fourth , the sum
of the first and second shall be to the second , as the sum of the third and fourth is
to the fourth . Given AE to EB as CF to FD , four magnitudes : then AE + EB : EB ...
B D E F A 18 Th . If the first be to the second as the third is to the fourth , the sum
of the first and second shall be to the second , as the sum of the third and fourth is
to the fourth . Given AE to EB as CF to FD , four magnitudes : then AE + EB : EB ...
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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 |
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 |