## Introductory Modern Geometry of Point, Ray, and Circle |

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ABCD Algebra altitude anti-parallelogram bisect called central angle central symmetry centre of similitude centre of symmetry chord circle K circumcircle circumscribed collinear concur congruent conjugate construct conversely corresponding cosine Data diagonal diameter dimensions distances divide draw a circle drawn Elementary Algebra encyclic equidistant fixed point geometric given point given ray half-rays harmonic hence homœoidal hypotenuse innerly inscribed intercepts intersection inverse join Let the student magnitude maxima and minima medial metric numbers mid-normal mid-points mid-rays normal opposite angles opposite sides outer outerly pairs parallel parallelogram perimeter plane points of touch polar pole polygon position power-axis Problem Proof proportion Q. E. D. Corollary radius ratio reciprocal rectangle regular n-side rhombus right angle round angle Scholium secant similar figures sine Solution Space square straight angle subtended surface symmetric tangent Theorem tract Trigonometry vertex vertices

### Popular passages

Page 36 - Two triangles are congruent if two angles and the included side of one are equal respectively to two angles and the included side of the other.

Page 95 - A circle is a closed plane curve, all points of which are equidistant from a point within called the center.

Page 35 - A having two sides and the included angle of the one equal respectively to two sides and the included angle of the other are congruent.

Page 252 - The area of any polygon circumscribing a circle is equal to half the product of the radius of the circle, and the perimeter of the polygon. (Divide the polygon into triangles, with the centre for vertex.) tEx.

Page 148 - Hence it is evident, that every visible right-lined triangle, will coincide in all its parts with some spherical triangle. The sides of the one will appear equal to the sides of the other, and the angles of the one to the angles of the other, each to each •, and therefore the whole of the one triangle will appear equal to the whole of the other. In a word, to the eye they will be one and the same, and have the same mathematical properties. The properties therefore of visible right-lined triangles,...

Page 185 - The triangles on each side of the perpendicular are similar to the -whole triangle and to each other. II. The perpendicular is a mean proportional between the segments of the hypotenuse. III. Each side about the right angle is a mean proportional between the hypotenuse and the adjacent segment.