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 7
... wherefore AL and BC are each of them equal to BG : and things that are equal to the same thing are equal to one another ; therefore the straight line † 1 Ax . AL is equal to BC . Wherefore , from the given point A , a straight line AL ...
... wherefore AL and BC are each of them equal to BG : and things that are equal to the same thing are equal to one another ; therefore the straight line † 1 Ax . AL is equal to BC . Wherefore , from the given point A , a straight line AL ...
Página 8
... wherefore the base BC shall coincide with the base EF ; because , the point B coin- ciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impossible ...
... wherefore the base BC shall coincide with the base EF ; because , the point B coin- ciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impossible ...
Página 10
... Wherefore , if B C COROLLARY . - Hence , every equiangular triangle is also equilateral . See N. + Hyp . * 5. 1 ... wherefore upon E / F the angle FDC is likewise greater than 10 EUCLID'S ELEMENTS .
... Wherefore , if B C COROLLARY . - Hence , every equiangular triangle is also equilateral . See N. + Hyp . * 5. 1 ... wherefore upon E / F the angle FDC is likewise greater than 10 EUCLID'S ELEMENTS .
Página 12
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal to it . Therefore , if two triangles ... wherefore , the given rectilineal angle BAC is bisected by the straight line AF . Which was to be done . PROPOSITION X ...
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal to it . Therefore , if two triangles ... wherefore , the given rectilineal angle BAC is bisected by the straight line AF . Which was to be done . PROPOSITION X ...
Página 13
... Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Which was to be done . COR . - By help of this problem it may be demonstrated , that two straight lines cannot have a common ...
... Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Which was to be done . COR . - By help of this problem it may be demonstrated , that two straight lines cannot have a common ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Visualização integral - 1814 |
Palavras e frases frequentes
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
Passagens conhecidas
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.