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 64
angle ; Therefore each of the angles AFE , BFE is a right angle ; wherefore the
straight line CD , A B drawn through the centre bisecting AB , which does not
pass through the centre , çuts AB at right angles . Again , let CD cut AB at right
angles ...
angle ; Therefore each of the angles AFE , BFE is a right angle ; wherefore the
straight line CD , A B drawn through the centre bisecting AB , which does not
pass through the centre , çuts AB at right angles . Again , let CD cut AB at right
angles ...
Σελίδα 65
Let the two circles ABC , CDG cat one another in the points B , C ; they have not
the same centre . For , if it be possible , let E be their centre : join EC , and draw
any straight line EFG meeting the circles C in F and G : and because E is the ...
Let the two circles ABC , CDG cat one another in the points B , C ; they have not
the same centre . For , if it be possible , let E be their centre : join EC , and draw
any straight line EFG meeting the circles C in F and G : and because E is the ...
Σελίδα 68
If a point be taken within a circle , from which there fall more than two equal
straight lines upon the circumference , that point is the centre of the circle . Let the
point D be taken within the circle ABC , from which there fall on the circumference
...
If a point be taken within a circle , from which there fall more than two equal
straight lines upon the circumference , that point is the centre of the circle . Let the
point D be taken within the circle ABC , from which there fall on the circumference
...
Σελίδα 71
IC F Take E the centre of the circle ABDC , and froin it draw EF , EG ,
perpendiculars to AB . ... thie straight line EF passing through the cenfre , cuts the
straight line AB , which does not pass through the centre at right angles , it also
bisects ( 3.
IC F Take E the centre of the circle ABDC , and froin it draw EF , EG ,
perpendiculars to AB . ... thie straight line EF passing through the cenfre , cuts the
straight line AB , which does not pass through the centre at right angles , it also
bisects ( 3.
Σελίδα 74
If a straight line touch a circle , the straight line drawn from the centre to the point
of contact , is perpendicular to the line touching the circle . 1 Let the straight line
DE touch the circle ABC in the point C ; take the centre F , and draw the straight ...
If a straight line touch a circle , the straight line drawn from the centre to the point
of contact , is perpendicular to the line touching the circle . 1 Let the straight line
DE touch the circle ABC in the point C ; take the centre F , and draw the straight ...
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
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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 |