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 σελίδες |
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Σελίδα 7
... given angle be less than a right angle . Draw CE perpendicular to AB ; let a line , C D , revolve about the point C , and let it first coincide with C A. At first the angle A CD is zero , and therefore less than the given angle , and it ...
... given angle be less than a right angle . Draw CE perpendicular to AB ; let a line , C D , revolve about the point C , and let it first coincide with C A. At first the angle A CD is zero , and therefore less than the given angle , and it ...
Σελίδα 39
... angle is constant . Let AB , AC be the straight lines intersecting in A. Let C be a point in A C , and C D its ... given length , C D. We have shown that the sum of the distances of any point on B C is equal to C D , and the sum of the ...
... angle is constant . Let AB , AC be the straight lines intersecting in A. Let C be a point in A C , and C D its ... given length , C D. We have shown that the sum of the distances of any point on B C is equal to C D , and the sum of the ...
Σελίδα 40
... angle BAC , have the difference of their distances equal to some line , R S , greater than CD . Consequently C N ... given point to a given straight line is the line bisecting at right angles the perpendicular from the given point to the ...
... angle BAC , have the difference of their distances equal to some line , R S , greater than CD . Consequently C N ... given point to a given straight line is the line bisecting at right angles the perpendicular from the given point to the ...
Σελίδα 47
... then join P D , D E , E P. It will readily be proved that PD , DE make equal angles with A B , and D E , E P make equal angles with A C. Hence PDEP is the angle required . 3. Through a given point draw a straight line which Theorems on Loc ...
... then join P D , D E , E P. It will readily be proved that PD , DE make equal angles with A B , and D E , E P make equal angles with A C. Hence PDEP is the angle required . 3. Through a given point draw a straight line which Theorems on Loc ...
Σελίδα 49
Richard Wormell. 3. Through a given point draw a straight line which shall make equal angles with two intersecting lines . Let AB , AC be the straight lines and G the given point . Draw A M bisecting the angle BA C , and through G draw ...
Richard Wormell. 3. Through a given point draw a straight line which shall make equal angles with two intersecting lines . Let AB , AC be the straight lines and G the given point . Draw A M bisecting the angle BA C , and through G draw ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 53 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Σελίδα 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.
Σελίδα 78 - To construct a circle which shall pass through two given points and touch a given straight line.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 30 - Any line drawn through the point of intersection of the diagonals of a parallelogram divides it into two equal quadrilaterals.
Σελίδα 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.