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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Resultat 6-10 av 61
Side 45
... BC , together with the square of AC , shall be equal to the square of the straight line made up of AB and BC together . Produce + AB to D , so that BD be equal † to CB ; and upon + 2 Post . AD , describe † the square AEFD ; and ...
... BC , together with the square of AC , shall be equal to the square of the straight line made up of AB and BC together . Produce + AB to D , so that BD be equal † to CB ; and upon + 2 Post . AD , describe † the square AEFD ; and ...
Side 49
... square of AE , is equal to the square of EF : but EF is equal to EB ; therefore the rectangle CF , FA , together ... BC produced : the square of AB shall be greater than the squares of AC , CB , by twice the rectangle BC , CD . Because ...
... square of AE , is equal to the square of EF : but EF is equal to EB ; therefore the rectangle CF , FA , together ... BC produced : the square of AB shall be greater than the squares of AC , CB , by twice the rectangle BC , CD . Because ...
Side 50
... square of DA ; therefore the squares of BD , DA are equal † to the squares of BC , CD , DA , and twice the rectangle BC , CD : but the square of BA is equal to the squares of BD , DA , because the angle at D is a right angle ; and the ...
... square of DA ; therefore the squares of BD , DA are equal † to the squares of BC , CD , DA , and twice the rectangle BC , CD : but the square of BA is equal to the squares of BD , DA , because the angle at D is a right angle ; and the ...
Side 51
... square of BC ; there- fore the squares of AB , BC are equal to the square of AC , † 2 Ax . and twice the square of BC , and twice the rectangle BC , CD : but because BD is di- vided into two parts in C , the rectangle , DB , BC is equal ...
... square of BC ; there- fore the squares of AB , BC are equal to the square of AC , † 2 Ax . and twice the square of BC , and twice the rectangle BC , CD : but because BD is di- vided into two parts in C , the rectangle , DB , BC is equal ...
Side 65
... square of FE is equal to the square of EG , because FE is equal to EG ; † Hyp . therefore the remaining square of AF ... BC be nearer to the centre than FG : AD shall be greater than any straight line BC , which is not a diameter , and ...
... square of FE is equal to the square of EG , because FE is equal to EG ; † Hyp . therefore the remaining square of AF ... BC be nearer to the centre than FG : AD shall be greater than any straight line BC , which is not a diameter , and ...
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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.