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 73
Also it is evident that there can be but one straight line which touches the circle in
the same point . PROP . XVII . PROB . D To draw a straight line from a given point
, either without or in the circumference , which shall touch a given circle .
Also it is evident that there can be but one straight line which touches the circle in
the same point . PROP . XVII . PROB . D To draw a straight line from a given point
, either without or in the circumference , which shall touch a given circle .
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 ...
Σελίδα 82
Let the straight line EF touch the circle ABCD in B , and from the point B let the
straight line BD be drawn cutting the circle : The angles whieh B ) makes with the
touching line EF , shall be equal to the angles in the alternate segments of the ...
Let the straight line EF touch the circle ABCD in B , and from the point B let the
straight line BD be drawn cutting the circle : The angles whieh B ) makes with the
touching line EF , shall be equal to the angles in the alternate segments of the ...
Σελίδα 85
ED = GE.EH ; therefore AE.EC = BE.ED. A Wherefore , if two straight lines , & c . Q
. E , D. H D F + PROP . XXXVI . THEOR . If from any point without a circle two
straight lines be drawn , one of which cuts the circle , and the other touches it ; the
...
ED = GE.EH ; therefore AE.EC = BE.ED. A Wherefore , if two straight lines , & c . Q
. E , D. H D F + PROP . XXXVI . THEOR . If from any point without a circle two
straight lines be drawn , one of which cuts the circle , and the other touches it ; the
...
Σελίδα 87
DC , be equal to the square of DB , DB toucbes the circle . Draw ( 17. 3. ) i be
straight line DE touching the circle ABC ; find the centre F , and join FE , FB , FD ;
then FED is a right ( 18. 3. ) angle : and because DE touches the circle ABC , and
...
DC , be equal to the square of DB , DB toucbes the circle . Draw ( 17. 3. ) i be
straight line DE touching the circle ABC ; find the centre F , and join FE , FB , FD ;
then FED is a right ( 18. 3. ) angle : and because DE touches the circle ABC , and
...
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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 |