## Modern geometry [ed.] with an appendix by W.B. Jack1876 |

### Dentro del libro

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**extremities**of a line are termed points . Points , like lines , have no thickness , and only mark position ; but , unlike lines , they have no length either , and , having neither length nor breadth , they possess no magnitude FIG . 3 ... Página 3

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**extremities**; as the line A B , for example ( Fig . 4 ) . The length of the straight line , A B , is also termed the ...**extremity**and a weight be suspended from the other , the thread will hang along a straight line , the ... Página 6

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**extremity**of the first must be placed on an**extremity**of the second ; 2 , The direction of the one must be made to coincide with the direction of the other . This being done , the position of the superposed line is completely determined ... Página 7

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**extremities**, and carrying the compasses to the scale . If one point be placed at the beginning of the scale , the numbers opposite the other will give the length of the line . A line longer than the scale may be measured by marking off ... Página 8

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**extremities**A and B , and then send an assistant to some point between A and B with a third rod . Let him move this rod until , on looking from A towards B , the rod at A hides from view both the others ; the third rod is then on the ...### Otras ediciones - Ver todas

Modern Geometry [Ed.] with an Appendix by W.B. Jack Richard Wormell Sin vista previa disponible - 2016 |

### Términos y frases comunes

A B and C D A B C D adjacent angles alternate angles angles equal angular points base bisector centre chord circumference circumscribing circle Construct a triangle contra-positive converse decagon describe a circle diameter distance divided draw a straight extremities figure fixed point fulfils the given given angle given circle given condition given straight line gonals greater Hence hypothenuse inches inscribed inscribed angle inscribed circle interior angles isosceles triangle less Let A B C line A B locus of points magnitudes middle points number of sides opposite angles opposite sides parallel parallelogram perpendicular point of contact point of intersection PROBLEM propositions proved quadrilateral ratio rect rectangle contained regular polygon respectively equal rhombus right angles right-angled triangle segment semicircle side opposite square on A B tangent termed Theo THEOREMS ON CHAPTER triangles are equal vertical angle

### Pasajes populares

Página 242 - 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 240 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Página 240 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Página 242 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Página 242 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.

Página 241 - If the first has to the second the same ratio which the third has to the fourth...

Página 240 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Página 242 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

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 239 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.