Modern geometry [ed.] with an appendix by W.B. Jack1876 |
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Σελίδα 15
... point on the earth's surface is the direction of the plumb - line at that point , and that a horizontal line is a line ... middle board , and a plumb - line is attached to a point , C , in this line . When the edge AB is horizontal , the ...
... point on the earth's surface is the direction of the plumb - line at that point , and that a horizontal line is a line ... middle board , and a plumb - line is attached to a point , C , in this line . When the edge AB is horizontal , the ...
Σελίδα 28
... points of intersection of these circles ; and , by means of the compasses ... middle point of A C , and call it M. Join M B. Finally measure A C. Also ... points whose distance shall be less than an inch ; and then find a point which ...
... points of intersection of these circles ; and , by means of the compasses ... middle point of A C , and call it M. Join M B. Finally measure A C. Also ... points whose distance shall be less than an inch ; and then find a point which ...
Σελίδα 35
... point B may fall on E , and BA along ED ; then , be- cause △ A B C = △ D E F by hypothesis , B C will fall along E F. Because B C E F by hypothesis , the point ... middle point of the side A C , and suppose the line BF B drawn and produced ...
... point B may fall on E , and BA along ED ; then , be- cause △ A B C = △ D E F by hypothesis , B C will fall along E F. Because B C E F by hypothesis , the point ... middle point of the side A C , and suppose the line BF B drawn and produced ...
Σελίδα 40
... middle of the tie - beam , and it must make equal angles with the principals.— Exercise 11 , p . 45 . Easy Exercises . ( a ) . With the point A as centre , and with a radius of one inch , describe a circle ; and then , with B as centre ...
... middle of the tie - beam , and it must make equal angles with the principals.— Exercise 11 , p . 45 . Easy Exercises . ( a ) . With the point A as centre , and with a radius of one inch , describe a circle ; and then , with B as centre ...
Σελίδα 43
... middle point of the base , will pass through the vertex and bisect the angle at the vertex . 13. When two isosceles triangles stand on the same base , the straight line which passes through their vertices will bisect the base and be ...
... middle point of the base , will pass through the vertex and bisect the angle at the vertex . 13. When two isosceles triangles stand on the same base , the straight line which passes through their vertices will bisect the base and be ...
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 C base bisect bisector called centre CHAPTER chord circle circumference common consequently Construct converse corresponding curve DEFINITIONS describe describe a circle determined diagonals diameter difference direction distance divided draw drawn equal equidistant evident example EXERCISE extremities fall figure four given circle given point given straight line greater half height Hence inches inscribed isosceles joining length less line joining magnitudes mark means measure meet middle points moving number of sides opposite opposite sides parallel parallelogram pass perpendicular plane position PROBLEM produced Proof properties proportion propositions proved quadrilateral radius ratio rect rectangle regular polygon respectively right angles segment sides similar square statements Suppose surface tangent termed Theorem third touch triangle true truth twice units whole yards
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.