Exercises on the geometry and measurement of plane figures, being solutions of the theorems, problems and questions in 'Wormell's Modern geometry'.Thomas Murby, 1883 - 192 páginas |
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Página 41
... circumference of a circle , so as always to be parallel to a given straight line : show that the locus of the extremities is a circle . D Let A be the centre of the circle and AD the radius . Let A B be parallel to the given straight ...
... circumference of a circle , so as always to be parallel to a given straight line : show that the locus of the extremities is a circle . D Let A be the centre of the circle and AD the radius . Let A B be parallel to the given straight ...
Página 42
... circumference of a given circle . B Let A B be one line joining the fixed point A to a point , B , on the circum- ference . Let D be its middle point , and let C be the middle point of the line , AO , joining the fixed point A with the ...
... circumference of a given circle . B Let A B be one line joining the fixed point A to a point , B , on the circum- ference . Let D be its middle point , and let C be the middle point of the line , AO , joining the fixed point A with the ...
Página 68
... circumference on the arc BD are equal , .. △ BAD = △ B C D , But because A B and C D are parallel , .. PBA BCD ; = 4 BAP = △ ABP . Hence △ APB is isosceles and the perpendicular from the apex to the base bisects the base ; there ...
... circumference on the arc BD are equal , .. △ BAD = △ B C D , But because A B and C D are parallel , .. PBA BCD ; = 4 BAP = △ ABP . Hence △ APB is isosceles and the perpendicular from the apex to the base bisects the base ; there ...
Página 69
... BDC - ZABD , and therefore E is half the angle at the centre on the difference of the intercepted arcs . 74. The locus of the middle points of chords drawn from the same point in the circumference is a The Circle . 69.
... BDC - ZABD , and therefore E is half the angle at the centre on the difference of the intercepted arcs . 74. The locus of the middle points of chords drawn from the same point in the circumference is a The Circle . 69.
Página 70
Richard Wormell. drawn from the same point in the circumference is a circumference . Let A B be a chord and AC a diameter from A. Let D be the middle point of A B. Join D to the centre O , and also join BC , then DO is parallel to BC ...
Richard Wormell. drawn from the same point in the circumference is a circumference . Let A B be a chord and AC a diameter from A. Let D be the middle point of A B. Join D to the centre O , and also join BC , then DO is parallel to BC ...
Términos y frases comunes
A B and C D ABCD adjacent angles bisect the angle centre chord circum circumference common tangents Consequently Construct a triangle DAB+ Decagon describe a circle diagonals diameter equal to half equilateral triangle Find the area given angle given circle given radius given side given straight line gonals greater Hence hypothenuse inscribed circle isosceles triangle joining the middle LADC line joining line parallel middle line middle point opposite angles parallel to A B parallelogram pendicular pentagon perimeter perpendicular bisector perpendicular to A B point of intersection polygon quadrilateral R₁ radii radius a circle rectangle regular polygon required circle respectively equal rhombus right angle right-angled triangle square tangent touch a given triangle A B D triangle required vertex
Pasajes populares
Página 91 - If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts.
Página 98 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.
Página 53 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Página 40 - Thus, of all straight lines drawn from a given point to a given straight line, that which is perpendicular to the given line is a minimum.
Página 78 - To construct a circle which shall pass through two given points and touch a given straight line.
Página 90 - Two triangles are equal when they have two sides and the included angle of the one, respectively equal to two sides and the included angle of the other.
Página 159 - A field in the form of a right-angled triangle is to be divided between two persons, by a fence made from the right angle meeting the hypothenuse perpendicularly, at the distance of 880 links from one end ; required the area of each person's share, the length of the division-fence being 660 links. Ans. 2a. 3r.
Página 9 - If from any point within a triangle, two straight lines be drawn to the extremities of either side, their sum will be less than Hie sum of the two other sides of the triangle.
Página 30 - Any line drawn through the point of intersection of the diagonals of a parallelogram divides it into two equal quadrilaterals.
Página 46 - Ft, and to Dd. 23. The common intersection of the three lines divides each into two parts, one of which is double of the other, and this point is the vertex of three triangles which have lines drawn from it to the bisection of the bases. Apply Euc. n. 12, 13. 24. Apply Theorem 3, p.