 | Henry Parr Hamilton - Conic sections - 1843 - 318 pages
...the Point in which two Lines MN', NM' meet ............... tb. The three Lines drawn from the Angles of a Triangle to the Middle Points of the opposite Sides meet in the same Point ................ ib. The Lines bisecting the three Angles of any Triangle meet in the... | |
 | Isaac Todhunter - Geometry - 1855 - 332 pages
...this chapter by applying them to prove some properties of a triangle. The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. Let ABC be a triangle, D, E, F, the middle points of the sides ; take A for the origin, AB for the... | |
 | Isaac Todhunter - Conic sections - 1858 - 334 pages
...this chapter by applying them to prove some properties of a triangle. The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. Let ABC be a triangle, D, JE, F, the middle points of the sides ; take A for the origin, AB for the... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...equally distant from the centre are equal to one another. 2. The straight lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. 3. Calculate by logarithms, 23-42 x -22652 , . 21 x (000256)* l ' 7000 X -006084 4. Find x and y from... | |
 | John Mulcahy - Geometry - 1862 - 252 pages
...Lemma 2° of Art. 9. 7°. It is evident from Art. 9, Lemma 1 , that the lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. It is easily proved also that they insect each other. For, if AE and BD be the bisectors of two of... | |
 | W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...KB, AL meet in a point. 30. Prove by taking two sides for axes that the lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. 31. A point moves so that the sum of the squares of its distances from two points x^y^ x 2 y 2 is equal... | |
 | George Holmes Howison, Joseph Ray - Geometry, Analytic - 1869 - 622 pages
...is a line passing through the intersection of «+/? and 276. Theorem. — The three lines which join the vertices of a triangle to the middle points of the opposite sides meet in one point. ANALYTIC GEOMETRY. 277. Theorem. — The three perpendiculars let fall from the vertices... | |
 | George Holmes Howison - Geometry, Analytic - 1869 - 622 pages
...the point midway between xf'y" and x"'y'"; or, show that, in general, the equations to the lines from the vertices of a triangle to the middle points of the opposite sides are (y" +/"-2/ )*-(*" +x"'-2x' }y+(x" y' -y" x' ) + (x'"y' -y"'x' )=0, (y"'+y' — 2y )x—(x'"+x'... | |
 | James Maurice Wilson - 1872 - 160 pages
...Prove that the three bisectors of the angles of a triangle are concurrent. IV.] TRANSVERSALS. 63 3. Prove that the lines joining the vertices of a triangle to the points of contact of the inscribed circle are concurrent. 4. Prove that the three perpendiculars of... | |
 | Braithwaite Arnett - Mathematics - 1873 - 120 pages
...right angles to A C. Thus the proposition is true. PROP. IV. The straight lines drawn from the angles of a triangle to the middle points of the opposite sides meet •in a point. Let D, E, F be the middle points of the sides BC, CA, AB of the triangle ABC, and join AD, BE meeting... | |
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The straight lines joining the vertices of a triangle to the middle points of the opposite sides meet in a point* which is for each line the point of trisection further from the vertex. 
