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 157
the polygon ABCDEF is to the palygon GHIKLM as the square of AB to the square
of GH ; but because the triangles ANB , GOH are equiangular , the square of AB
is to the square of GH as the square of A N to the square of GO ( 4. 6. ) , or as ...
the polygon ABCDEF is to the palygon GHIKLM as the square of AB to the square
of GH ; but because the triangles ANB , GOH are equiangular , the square of AB
is to the square of GH as the square of A N to the square of GO ( 4. 6. ) , or as ...
Σελίδα 158
1. ) ; wherefore , the point M is in the circumference of the circle ; and because
KMG is a right angle , KM touches the circle . And in the same man . ner , by
joining the centre and the other angular points of the inscribed polygon , an
equilateral ...
1. ) ; wherefore , the point M is in the circumference of the circle ; and because
KMG is a right angle , KM touches the circle . And in the same man . ner , by
joining the centre and the other angular points of the inscribed polygon , an
equilateral ...
Σελίδα 159
Let the polygon described about the circle be called , M and the polygon
inscribed be called N ; then , B L F M H с G D because these polygons are similar
( Cor . 3. 1. ) , they are as the squares of the homologous sides , HL and AF ( Sup.
3 .
Let the polygon described about the circle be called , M and the polygon
inscribed be called N ; then , B L F M H с G D because these polygons are similar
( Cor . 3. 1. ) , they are as the squares of the homologous sides , HL and AF ( Sup.
3 .
Σελίδα 160
has been demonstrated , that the square of AC is to the square of AN as the
polygon M to the difference of the polygons ; therefore , since the square of AC is
greater than M , the square of AF is greater than the difference of the polygons (
14.
has been demonstrated , that the square of AC is to the square of AN as the
polygon M to the difference of the polygons ; therefore , since the square of AC is
greater than M , the square of AF is greater than the difference of the polygons (
14.
Σελίδα 162
And as the same is true of all the other triangles having their vertices in D , which
make up the inscribed polygon , therefore the whole of the inscribed polygon is
less than the rectangle contained by DA , and AK half the perimeter of the ...
And as the same is true of all the other triangles having their vertices in D , which
make up the inscribed polygon , therefore the whole of the inscribed polygon is
less than the rectangle contained by DA , and AK half the perimeter of the ...
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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 |