Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |
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Σελίδα 67
In like manger it may be shown that FD is greater than CD . Therefore DA is the
greatest ; and DE greater than DF , and DF than DC . And because MK , KD are
greater ( 20. 1. ) than MD , and MK is equal to MG , the remainder KD is greater (
5.
In like manger it may be shown that FD is greater than CD . Therefore DA is the
greatest ; and DE greater than DF , and DF than DC . And because MK , KD are
greater ( 20. 1. ) than MD , and MK is equal to MG , the remainder KD is greater (
5.
Σελίδα 93
of the angles ABC , BCD , CDA is a right angle ; therefore the quadrilateral figure
ABCD is rectangular , and it has been shown to be equilateral ; therefore it is a
square ; and it is inseribed in the circle ABCD . Which was to be done . PROP .
of the angles ABC , BCD , CDA is a right angle ; therefore the quadrilateral figure
ABCD is rectangular , and it has been shown to be equilateral ; therefore it is a
square ; and it is inseribed in the circle ABCD . Which was to be done . PROP .
Σελίδα 98
to the other sides , and the third angle to the third angle : therefore the straight
line KC is equal to CL , and the angle FKC to the angle FLC : and because KC is
equal to CL , KL is double of KC : in the same manner , it may be shown that HK
is ...
to the other sides , and the third angle to the third angle : therefore the straight
line KC is equal to CL , and the angle FKC to the angle FLC : and because KC is
equal to CL , KL is double of KC : in the same manner , it may be shown that HK
is ...
Σελίδα 151
Now it has been shown that FB : BE :: AD : DE , therefore FB : BE :: FA : AE ,
Therefore , & c . Q. E. D. Cor . If AB be drawn , because FB : BE :: FA : AE , the
angle FBE is bisected ( 3.6 . ) by AB . Also , since FD : DC :: DC : DE , by
composition ...
Now it has been shown that FB : BE :: AD : DE , therefore FB : BE :: FA : AE ,
Therefore , & c . Q. E. D. Cor . If AB be drawn , because FB : BE :: FA : AE , the
angle FBE is bisected ( 3.6 . ) by AB . Also , since FD : DC :: DC : DE , by
composition ...
Σελίδα 309
But , as was shown K : L :: C : D , by conversion and alternation ; K - C : K :: L - D :
L , therefore , ex æquo , A + K : K :: B + L : L ... The same may be shown , if K is
less than C ; therefore in every case there are conditions necessary to the truth of
...
But , as was shown K : L :: C : D , by conversion and alternation ; K - C : K :: L - D :
L , therefore , ex æquo , A + K : K :: B + L : L ... The same may be shown , if K is
less than C ; therefore in every case there are conditions necessary to the truth of
...
Τι λένε οι χρήστες - Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common contained cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved Q. E. D. PROP radius ratio reason rectangle contained rectilineal figure right angles segment shown sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Σελίδα 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.
Σελίδα 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Σελίδα 30 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Σελίδα 51 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Σελίδα 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |
| Συγγραφείς | Euclid, John Playfair |
| Επιμελητής | John Playfair |
| Έκδοση | 7 |
| Εκδότης | Marot & Walter, 1826 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Μέγεθος | 320 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |