Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ... |
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Σελίδα 67
... and being every way isosceles , it is also equiangular ( e ) : therefore , the
angle CGD is one third of two right angles ( f ) , EGD is also one third of the same
; and because the straight line EG makes with CF , the adjacent angles equal to
two ...
... and being every way isosceles , it is also equiangular ( e ) : therefore , the
angle CGD is one third of two right angles ( f ) , EGD is also one third of the same
; and because the straight line EG makes with CF , the adjacent angles equal to
two ...
Σελίδα 69
A. There is a series of multiples ; as , the first , second , third , & c . , of which ,
waving the etyinology of the word , the magnitude itself is the first , its double is
the second , its triple the third , & c . B. A magnitude may have one , two , or three
...
A. There is a series of multiples ; as , the first , second , third , & c . , of which ,
waving the etyinology of the word , the magnitude itself is the first , its double is
the second , its triple the third , & c . B. A magnitude may have one , two , or three
...
Σελίδα 71
... E + F : therefore AG + CH + GB + HDAB + CD = 2 ( E + F ) , ( b ) . In like manner
, it AB , CD were third multiples of E , F , their sum would be third multiples of the
sum of E and F ; and so of any equimultiples whatever . Also , if there were three
...
... E + F : therefore AG + CH + GB + HDAB + CD = 2 ( E + F ) , ( b ) . In like manner
, it AB , CD were third multiples of E , F , their sum would be third multiples of the
sum of E and F ; and so of any equimultiples whatever . Also , if there were three
...
Σελίδα 72
3 Th . If the first be the same multiple of the second which the third is of the fourth ;
and if of the first and third equimultiples be taken , these shall be equimultiples ,
one of the second the other of the fourth . Let A , B , C , D be four magnitudes , in
...
3 Th . If the first be the same multiple of the second which the third is of the fourth ;
and if of the first and third equimultiples be taken , these shall be equimultiples ,
one of the second the other of the fourth . Let A , B , C , D be four magnitudes , in
...
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
...
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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 |