Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ... |
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Σελίδα 81
CAL E Th . Of four proportionals , the first is to its excess above the second as the
third is to its excess above the fourth . Given AB : BE :: CD : DF ; then , by hyp . ,
AB : AB - BE :: CD : CD - DF . Let the parts of AB be AE , EB , and the parts of CD
...
CAL E Th . Of four proportionals , the first is to its excess above the second as the
third is to its excess above the fourth . Given AB : BE :: CD : DF ; then , by hyp . ,
AB : AB - BE :: CD : CD - DF . Let the parts of AB be AE , EB , and the parts of CD
...
Σελίδα 119
8 Th . Four rectangles of two sides of a triangle is to the rectangle of the whole
perimeter and the excess of the two sides above the base , as the square of
radius is to the square of the cosine of half the angle contained by those sides .
8 Th . Four rectangles of two sides of a triangle is to the rectangle of the whole
perimeter and the excess of the two sides above the base , as the square of
radius is to the square of the cosine of half the angle contained by those sides .
Σελίδα 120
BAC ) 2 ; and AD = AB , and MNVNL = the excess of the two sides above the
base . Wherefore , four rectangles , 8 Q. E. D. 9 Th . In any triangle , the less of
two given sides is to the greater , as radius is to the tangent of an angle greater
than ...
BAC ) 2 ; and AD = AB , and MNVNL = the excess of the two sides above the
base . Wherefore , four rectangles , 8 Q. E. D. 9 Th . In any triangle , the less of
two given sides is to the greater , as radius is to the tangent of an angle greater
than ...
Σελίδα 127
Take in NO the part NP less than its half , and less than AĎ ; and let a polygon be
described about the circle ABC , so that its excess above ABC may be less than
the square of NP ( cor . 1 , p . 4 of this ) . Let the side of this polygon be EF .
Take in NO the part NP less than its half , and less than AĎ ; and let a polygon be
described about the circle ABC , so that its excess above ABC may be less than
the square of NP ( cor . 1 , p . 4 of this ) . Let the side of this polygon be EF .
Σελίδα 129
... the straight line composed of the radius and its excess above the subsine of
the arc : and the chord of the arc is a mean proportional between the diameter
and the subsine . B В Let C be the centre of the circle ABD ; let DB be any arc ,
and ...
... the straight line composed of the radius and its excess above the subsine of
the arc : and the chord of the arc is a mean proportional between the diameter
and the subsine . B В Let C be the centre of the circle ABD ; let DB be any arc ,
and ...
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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 |