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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Página 22
Postulate ) the circle BC ) , and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in D A B E which the circles cut one another , draw the straight lines ( 1. Post .
Postulate ) the circle BC ) , and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in D A B E which the circles cut one another , draw the straight lines ( 1. Post .
Página 23
Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . > From the greater of two given straight lines to cut off a part equal to the less ...
Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . > From the greater of two given straight lines to cut off a part equal to the less ...
Página 28
1. ) DB , and the straight line AB is divided into two equal parts in the point D. Which was to be done . 2 А D B PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in ...
1. ) DB , and the straight line AB is divided into two equal parts in the point D. Which was to be done . 2 А D B PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in ...
Página 29
To draw a straight line perpendicular to a given straight line , of an unlimited length , from a given point without it . Let AB be a given straight line , which may be produced to any length both ways , and let C be a point without it ...
To draw a straight line perpendicular to a given straight line , of an unlimited length , from a given point without it . Let AB be a given straight line , which may be produced to any length both ways , and let C be a point without it ...
Página 41
To draw a straight line through a given point parallel to a given straight line . Let A be the given point , and BC the given straight line ; it is res quired to draw a straight line through the point A , parallel to A. the straight ...
To draw a straight line through a given point parallel to a given straight line . Let A be the given point , and BC the given straight line ; it is res quired to draw a straight line through the point A , parallel to A. the straight ...
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Términos y frases comunes
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 exterior 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 proportional 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
Pasajes populares
Página 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.
Página 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.
Página 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Página 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...
Página 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...
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Información bibliográfica
| Título | 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 |
| Autor | John Playfair |
| Editor | G. Long, 1819 |
| Procedencia del original | Universidad de Michigan |
| Digitalizado | 11 Jun. 2007 |
| Largo | 333 páginas |
| Exportar cita | BiBTeX EndNote RefMan |