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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Side 236
... cone , and so on , there must at length remain some segments of the cone which are together less than the solid Z ; let these be the segments upon EO , OF , FP , PG , GR , RH , HS , SE : therefore the remainder of the cone , viz . the ...
... cone , and so on , there must at length remain some segments of the cone which are together less than the solid Z ; let these be the segments upon EO , OF , FP , PG , GR , RH , HS , SE : therefore the remainder of the cone , viz . the ...
Side 237
... cone AL to any solid which is less than the cone EN . In the same manner it may be demonstrated , that the circle EFGH is not to the circle ABCD , as the cone EN to any solid less than the cone AL . Nor can the circle ABCD be to the ...
... cone AL to any solid which is less than the cone EN . In the same manner it may be demonstrated , that the circle EFGH is not to the circle ABCD , as the cone EN to any solid less than the cone AL . Nor can the circle ABCD be to the ...
Side 238
... cone and let LAQ be one of the triangles containing the py- ramid upon the polygon ATBYCVDQ , the vertex of which is ... cone ABCDL is similar * 24 Def.11 . to the cone EFGHN , AC is * to EG as the axis KL to the axis MN ; and as AC to ...
... cone and let LAQ be one of the triangles containing the py- ramid upon the polygon ATBYCVDQ , the vertex of which is ... cone ABCDL is similar * 24 Def.11 . to the cone EFGHN , AC is * to EG as the axis KL to the axis MN ; and as AC to ...
Side 239
... cones , it may be demonstrated , that each pyramid in the first cone has to each in the other , taking them in the same order , the triplicate ratio of that which the side AK has to the side EN ; that is , which AC has to EG : but as ...
... cones , it may be demonstrated , that each pyramid in the first cone has to each in the other , taking them in the same order , the triplicate ratio of that which the side AK has to the side EN ; that is , which AC has to EG : but as ...
Side 240
... cone of which the base is the circle EFGH and vertex N , the triplicate ratio of that which AC has to EG . In the same manner it may be demonstrated , that neither has the cone EFGHN to any solid which is less than the cone ABCDL , the ...
... cone of which the base is the circle EFGH and vertex N , the triplicate ratio of that which AC has to EG . In the same manner it may be demonstrated , that neither has the cone EFGHN to any solid which is less than the cone ABCDL , the ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1814 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 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.
Side 22 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Side 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.
Side 5 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Side 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...
Side 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.
Side 89 - PBOR. —To describe an isosceles triangle, having each of the angles at the base, double of the third angle. Take any straight...
Side 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.