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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Página 15
... direction shall bisect the angle CPD , and the segments CO , OD shall bear a given ratio to each other . Take C'O and OD ′ ( fig . 7 ) in the given ratio , and describe the circle which is the locus of points whose distances from C ...
... direction shall bisect the angle CPD , and the segments CO , OD shall bear a given ratio to each other . Take C'O and OD ′ ( fig . 7 ) in the given ratio , and describe the circle which is the locus of points whose distances from C ...
Página 24
... directions of the principal axes , we have tan 20∞ , 0 = 45 ° . Now , transforming the equation to axes through same origin as last , but making an angle of 45 ° with them , our equation takes the form 3x2 + 2y2 = 6 ( see fig . 11 ) ...
... directions of the principal axes , we have tan 20∞ , 0 = 45 ° . Now , transforming the equation to axes through same origin as last , but making an angle of 45 ° with them , our equation takes the form 3x2 + 2y2 = 6 ( see fig . 11 ) ...
Página 36
... direction of motion at the two places respec- tively . Then we have and v , cose , v , cose , = v ... ( 1 ) = v , sin1 = v , sin 0 , -gt , v2 where t is the time between the two points ; therefore gtv , sin 0 , - v , sin e1 , and , by ...
... direction of motion at the two places respec- tively . Then we have and v , cose , v , cose , = v ... ( 1 ) = v , sin1 = v , sin 0 , -gt , v2 where t is the time between the two points ; therefore gtv , sin 0 , - v , sin e1 , and , by ...
Página 37
... direction in which it must be propelled in order to strike another ball in a given position after one , two , and three reflexions respectively from the vertical planes . Let Aa , Bb ( fig . 14 ) be the two vertical walls , C the ball ...
... direction in which it must be propelled in order to strike another ball in a given position after one , two , and three reflexions respectively from the vertical planes . Let Aa , Bb ( fig . 14 ) be the two vertical walls , C the ball ...
Página 42
... directions of the string on the moveable pulley are at right angles to each other , what is the greatest weight that can be raised by a man standing on the ground whose own weight is 12 stone , when he pulls at the free end of the ...
... directions of the string on the moveable pulley are at right angles to each other , what is the greatest weight that can be raised by a man standing on the ground whose own weight is 12 stone , when he pulls at the free end of the ...
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Solutions to the Mathematical Examination Papers Set for Admission to the ... D. Tierney,Handell Sharratt Sin vista previa disponible - 2016 |
Solutions To The Mathematical Examination Papers Set For Admission To The ... D. Tierney,Handell Sharratt Sin vista previa disponible - 2023 |
Términos y frases comunes
acceleration axes axis ball base bisection body cent centre circle coefficient common condition Conic contained cose curve Define described determine diameter difference direction distance Divide divisible draw drawn equal equation equilibrium expression feet focus forces four fraction gallons give given gravity half Hence inches inclined increases integration intersect Join least length limiting means Multiply obtain opposite original parabola parallel parallelogram Parkinson's Mechanics particle passing perpendicular places plane positive produced Prop prove radius ratio rectangle remainder represented respectively rest Result right angles roots seconds segments shew sides signs Similarly space square straight line string Subtract tangent triangle Trig unit velocity vertex vertical virtual weight whence yards
Pasajes populares
Página 55 - If two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 11 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Página 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.
Página 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.
Página 15 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 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.
Página 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.
Página 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.
Página 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.