Modern geometry [ed.] with an appendix by W.B. Jack1876 |
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Σελίδα 11
... vertex . To measure the magnitude of an angle , we have simply to consider what part of a whole revolution is required to carry one of the sides to the other . This has nothing whatever to do with the length of the sides . In Fig . 16 ...
... vertex . To measure the magnitude of an angle , we have simply to consider what part of a whole revolution is required to carry one of the sides to the other . This has nothing whatever to do with the length of the sides . In Fig . 16 ...
Σελίδα 16
... vertex , E ; such that the sides of one are the continuation of the sides of the other . Two such angles are called vertically - opposite angles . Vertically - opposite angles are equal ( Fig . 34 ) . The two statements here made admit ...
... vertex , E ; such that the sides of one are the continuation of the sides of the other . Two such angles are called vertically - opposite angles . Vertically - opposite angles are equal ( Fig . 34 ) . The two statements here made admit ...
Σελίδα 18
... vertex . 16. The magnitude of an angle is measured by the amount of revolution required to make one of the sides coincide with the other . 17. Adjacent angles are such as have a common vertex , and are on opposite sides of a common side ...
... vertex . 16. The magnitude of an angle is measured by the amount of revolution required to make one of the sides coincide with the other . 17. Adjacent angles are such as have a common vertex , and are on opposite sides of a common side ...
Σελίδα 25
... vertex of the angle as centre , is intercepted by the sides of the angle . Certain fractions of a circumference have special names : - The 360th part of a circumference is termed a Degree . The 60th part of a Degree is termed a Minute ...
... vertex of the angle as centre , is intercepted by the sides of the angle . Certain fractions of a circumference have special names : - The 360th part of a circumference is termed a Degree . The 60th part of a Degree is termed a Minute ...
Σελίδα 29
... vertex is at the centre is termed an angle at the centre , and is said to stand on the arc intercepted by its sides . THEOREM IV . In equal circles equal angles at the centre stand on equal arcs : And equal arcs subtend equal angles at ...
... vertex is at the centre is termed an angle at the centre , and is said to stand on the arc intercepted by its sides . THEOREM IV . In equal circles equal angles at the centre stand on equal arcs : And equal arcs subtend equal angles at ...
Άλλες εκδόσεις - Προβολή όλων
Modern Geometry [Ed.] with an Appendix by W.B. Jack Richard Wormell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 241 - If the first has to the second the same ratio which the third has to the fourth...
Σελίδα 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.
Σελίδα 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.
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 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.