The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson].1834 |
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Página 171
... cone is called a right - angled cone ; if it be less than the other side , an obtuse - angled ; and if greater , an acute - angled cone . XIX . The axis of a cone is the fixed straight line about which the triangle revolves . XX . The ...
... cone is called a right - angled cone ; if it be less than the other side , an obtuse - angled ; and if greater , an acute - angled cone . XIX . The axis of a cone is the fixed straight line about which the triangle revolves . XX . The ...
Página 232
... cone is the third part of a cylinder which has the same base and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude : the cone shall be the third part of the ...
... cone is the third part of a cylinder which has the same base and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude : the cone shall be the third part of the ...
Página 233
... cone : but this prism is triple of the pyramid upon the same base , of which the vertex is the same with the vertex of the cone ; therefore the pyramid upon the base AEBFCGDH , having the same vertex with the cone , is greater than the cone ...
... cone : but this prism is triple of the pyramid upon the same base , of which the vertex is the same with the vertex of the cone ; therefore the pyramid upon the base AEBFCGDH , having the same vertex with the cone , is greater than the cone ...
Página 234
... cone ; this pyramid is greater than the half of the cone ; because , as was before de- monstrated , if a square be described about the circle , the square ABCD is the half of it : and if upon these squares there be erected solid ...
... cone ; this pyramid is greater than the half of the cone ; because , as was before de- monstrated , if a square be described about the circle , the square ABCD is the half of it : and if upon these squares there be erected solid ...
Página 235
... cone , or , the cone is the third part of the cylinder . Wherefore , every cone , & c . Q. E. D. PROPOSITION XI . THEOR . - Cones and cylinders of the same altitude , are to one See N. another as their bases . Let the cones and ...
... cone , or , the cone is the third part of the cylinder . Wherefore , every cone , & c . Q. E. D. PROPOSITION XI . THEOR . - Cones and cylinders of the same altitude , are to one See N. another as their bases . Let the cones and ...
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Términos y frases comunes
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circle EFGH circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple parallel parallelogram perpendicular point F polygon prism Prop proportionals Q. E. D. PROPOSITION radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment shewn sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR.-If tiple triangle ABC vertex wherefore
Pasajes populares
Página 32 - 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...
Página 138 - 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.
Página 39 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 22 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Página 41 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 5 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Página 38 - IF a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided...
Página 262 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Página 89 - PBOR. —To describe an isosceles triangle, having each of the angles at the base, double of the third angle. Take any straight...
Página 165 - 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.