Solutions to the mathematical examination papers set for admission to the Royal military academy, Woolwich, and for the Royal military college [&c.] by D. Tierney and H. Sharratt1877 |
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Σελίδα 20
... Prop . 16 . If a straight line CD be parallel to a plane , prove that the intersection of any plane passing through CD with the given plane will lie in a straight line parallel to CD . Through CD ( fig . 9 ) drawn a plane parallel to ...
... Prop . 16 . If a straight line CD be parallel to a plane , prove that the intersection of any plane passing through CD with the given plane will lie in a straight line parallel to CD . Through CD ( fig . 9 ) drawn a plane parallel to ...
Σελίδα 23
... Props . V. , VIII . 9. Prove that the perpendiculars drawn from the foci of an ellipse on a tangent at any point intersect the tangent in the circumference of the circle described on the major axis . Drew , Conic Sections , Prop . xv ...
... Props . V. , VIII . 9. Prove that the perpendiculars drawn from the foci of an ellipse on a tangent at any point intersect the tangent in the circumference of the circle described on the major axis . Drew , Conic Sections , Prop . xv ...
Σελίδα 24
... Props . of Cone . 11. Given the equations to two straight lines referred to rectangular coordinates , find the angle at which they intersect . Salmon , Conic Sections , Art . 25 . Prove that the equation 3y2- 8xy - 3x2 - 29x + 3y - 18 ...
... Props . of Cone . 11. Given the equations to two straight lines referred to rectangular coordinates , find the angle at which they intersect . Salmon , Conic Sections , Art . 25 . Prove that the equation 3y2- 8xy - 3x2 - 29x + 3y - 18 ...
Σελίδα 44
D. Tierney. 9. A uniform beam of given weight rests upon a prop with one end against a smooth vertical wall and a weight is suspended from the other end of the beam ; find the position of equilibrium . Let AB ( fig . 17 ) be the rod , 2a ...
D. Tierney. 9. A uniform beam of given weight rests upon a prop with one end against a smooth vertical wall and a weight is suspended from the other end of the beam ; find the position of equilibrium . Let AB ( fig . 17 ) be the rod , 2a ...
Σελίδα 61
... Prop . 13 . 2. One circle cannot touch another on the inside in more points than one . Euclid , Book III . , Prop . 13 . 3. Divide a straight line into two parts , so that the rectangle contained by them may equal the square of the ...
... Prop . 13 . 2. One circle cannot touch another on the inside in more points than one . Euclid , Book III . , Prop . 13 . 3. Divide a straight line into two parts , so that the rectangle contained by them may equal the square of the ...
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Solutions to the Mathematical Examination Papers Set for Admission to the ... D. Tierney,Handell Sharratt Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Solutions To The Mathematical Examination Papers Set For Admission To The ... D. Tierney,Handell Sharratt Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
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Δημοφιλή αποσπάσματα
Σελίδα 55 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 71 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 11 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Σελίδα 12 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 13 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Σελίδα 15 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα 13 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Σελίδα 62 - In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle.
Σελίδα 13 - PROP. X. THEOR. IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Σελίδα 70 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.