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 iv
... demonstrated . But indeed this Proposition , which makes the 10th definition of the 11th Book , is not true universally , except in the case in which each of the solid angles of the figures is contained by no more than three plane ...
... demonstrated . But indeed this Proposition , which makes the 10th definition of the 11th Book , is not true universally , except in the case in which each of the solid angles of the figures is contained by no more than three plane ...
Side vi
... demonstrated to be given , and from these , other things are again shewn to be given , and so on , til that which was proposed to be found out in the problem demonstrated to be given ; and when this is done the pro- Elem is solved , and ...
... demonstrated to be given , and from these , other things are again shewn to be given , and so on , til that which was proposed to be found out in the problem demonstrated to be given ; and when this is done the pro- Elem is solved , and ...
Side vii
... demonstrated is assumed in the analysis ; but in the demonstrations of the Data , the thing to be demonstrated , which is , that something or other is given , is never once assumed in the demonstration , from which it is manifest , that ...
... demonstrated is assumed in the analysis ; but in the demonstrations of the Data , the thing to be demonstrated , which is , that something or other is given , is never once assumed in the demonstration , from which it is manifest , that ...
Side 9
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the remaining angle ABC is equal to the remaining angle ACB , which are the angles at † 3 Ax . the ...
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the remaining angle ABC is equal to the remaining angle ACB , which are the angles at † 3 Ax . the ...
Side 10
... demonstrated to be greater than it ; which is impossible . * But if one of the vertices , as D , be within the other triangle ACB , produce AC , AD to E , F : therefore , because , AC is equal to AD in the triangle ACD , the angles ECD ...
... demonstrated to be greater than it ; which is impossible . * But if one of the vertices , as D , be within the other triangle ACB , produce AC , AD to E , F : therefore , because , AC is equal to AD in the triangle ACD , the angles ECD ...
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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.