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 42
... 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 centre O. Join O B and C D. A Now CD is parallel and equal to half OB ( Example 43 ) ; hence D is at 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 centre O. Join O B and C D. A Now CD is parallel and equal to half OB ( Example 43 ) ; hence D is at the ...
Σελίδα 70
... when continued in the opposite direction let it meet the circum- ference in E. Draw the lines B E ,. BCE , and suppose B E to cut A D in F. Now BAC / BEC ; ... Z BAD = 2BED . Again in the triangles F E D and FA B 70 Theorems and Problems .
... when continued in the opposite direction let it meet the circum- ference in E. Draw the lines B E ,. BCE , and suppose B E to cut A D in F. Now BAC / BEC ; ... Z BAD = 2BED . Again in the triangles F E D and FA B 70 Theorems and Problems .
Σελίδα 71
... . 77. The feet of the perpendiculars drawn to the sides of a triangle from any point on the circum- ference which passes through its vertices lie in a straight line . Let A B C be the triangle , O the The Circle . 75.
... . 77. The feet of the perpendiculars drawn to the sides of a triangle from any point on the circum- ference which passes through its vertices lie in a straight line . Let A B C be the triangle , O the The Circle . 75.
Σελίδα 73
... circum- scribe a given circle of the same radius ? If the centres of two of the circles be joined together and to the centre of the given circle , an equilateral triangle will be formed , and the ques- tion will be resolved into finding ...
... circum- scribe a given circle of the same radius ? If the centres of two of the circles be joined together and to the centre of the given circle , an equilateral triangle will be formed , and the ques- tion will be resolved into finding ...
Σελίδα 77
... circum- scribed circle . Also , by Exercise 62 , O F , which is the radius of the inscribed circle , is half of C F the radius of the circumscribed circle . 85. The locus of the centres of the circles which are inscribed in all right ...
... circum- scribed circle . Also , by Exercise 62 , O F , which is the radius of the inscribed circle , is half of C F the radius of the circumscribed circle . 85. The locus of the centres of the circles which are inscribed in all right ...
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D ABCD base centre chord circum circumference Consequently Construct a triangle contained Continue describe describe a circle diagonals diameter difference distance divided draw drawn equal Example extremities figure Find the area formed four given angle given circle given length given point given radius given side given straight line greater half height Hence hypothenuse inscribed circle isosceles triangle less Let A B C line joining lines drawn locus meet middle line middle point parallel parallelogram pass pentagon perimeter perpendicular point of intersection polygon problem produced Prove quadrilateral radii rect rectangle right angle sides Similarly square Suppose Take triangle triangle required twice vertex vertical yards
Δημοφιλή αποσπάσματα
Σελίδα 93 - 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 100 - 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 54 - 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 80 - 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 161 - 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.