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 52
of the triangle ABD , because they are upon the same base BD , and between the
same parallels , BD , AL ; and the square GB is double of the triangle BFC ,
because these also are upon the same base FB , and between the game
parallels ...
of the triangle ABD , because they are upon the same base BD , and between the
same parallels , BD , AL ; and the square GB is double of the triangle BFC ,
because these also are upon the same base FB , and between the game
parallels ...
Σελίδα 61
To divide a given straight line into two parts , so that the rectangle contained by
the whole , and one of the parts , may be equal to the square of the other part .
Let AB be the given straight line ; it is required to divide it into two parts , so that
the ...
To divide a given straight line into two parts , so that the rectangle contained by
the whole , and one of the parts , may be equal to the square of the other part .
Let AB be the given straight line ; it is required to divide it into two parts , so that
the ...
Σελίδα 63
To describe a square that shall be equal to a given rectilineal figure . Let A be the
given rectilineal figure ; it is required to describe a .square that shall be equal to A
. Describe ( 45. 1. ) the rectangular parallelogram BCDE equal to the rectilineal ...
To describe a square that shall be equal to a given rectilineal figure . Let A be the
given rectilineal figure ; it is required to describe a .square that shall be equal to A
. Describe ( 45. 1. ) the rectangular parallelogram BCDE equal to the rectilineal ...
Σελίδα 76
to the square of AE , because the angle AFE is a right angle ; and , for the like
reason , the squares of EG , GC are equal to the square of EC : Therefore the
squares of AF , FE are equal to the squares of CG , GE , of which the square of AF
is ...
to the square of AE , because the angle AFE is a right angle ; and , for the like
reason , the squares of EG , GC are equal to the square of EC : Therefore the
squares of AF , FE are equal to the squares of CG , GE , of which the square of AF
is ...
Σελίδα 164
the polygon ABCDEF is to the polygon GHIKLM as the square of AB to the square
of GH ; but because the triangles ANB , GOH are equiangular , the square of AB
is square of GH as the square of AN to the square of GO ( 4. 6. ) , or as four ...
the polygon ABCDEF is to the polygon GHIKLM as the square of AB to the square
of GH ; but because the triangles ANB , GOH are equiangular , the square of AB
is square of GH as the square of AN to the square of GO ( 4. 6. ) , or as four ...
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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 cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid 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 shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Σελίδα 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Σελίδα 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 130 - 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 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...
Σελίδα 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
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 |
| Συγγραφέας | John Playfair |
| Επιμελητής | John Playfair |
| Μεταφράστηκε από | John Playfair |
| Έκδοση | 5 |
| Εκδότης | G. Long, 1819 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Μέγεθος | 333 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |