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 |
No interior do livro
Resultados 1-5 de 100
Página 4
... square is that which has all its sides equal , and all its angles right angles . XXXI . An oblong is that which has all its angles right angles , but has not all its sides equal . XXXII . A rhombus is that which has all its sides equal ...
... square is that which has all its sides equal , and all its angles right angles . XXXI . An oblong is that which has all its angles right angles , but has not all its sides equal . XXXII . A rhombus is that which has all its sides equal ...
Página 36
... square upon a given straight line . Let AB be the given straight line ; it is required to de- scribe a square upon AB . D * From the point A , draw * AC at right angles to AB , and make AD equal to AB ; through the point D , draw DE pa ...
... square upon a given straight line . Let AB be the given straight line ; it is required to de- scribe a square upon AB . D * From the point A , draw * AC at right angles to AB , and make AD equal to AB ; through the point D , draw DE pa ...
Página 37
... square described upon the side BC , shall be equal to the squares described upon BA , AC . • 46. 1 . 31. 1 . right angle , the 30 Def . On BC describe the square BDEC ; and on BA , AC , the squares GB , HC ; and through A , draw * AL ...
... square described upon the side BC , shall be equal to the squares described upon BA , AC . • 46. 1 . 31. 1 . right angle , the 30 Def . On BC describe the square BDEC ; and on BA , AC , the squares GB , HC ; and through A , draw * AL ...
Página 38
... square described upon BC , one of the sides of the triangle ABC , be equal to the squares upon the other sides BA ... square of DA is equal to the square of AB : to each of these add the square of AC ; therefore the squares of DA , AC ...
... square described upon BC , one of the sides of the triangle ABC , be equal to the squares upon the other sides BA ... square of DA is equal to the square of AB : to each of these add the square of AC ; therefore the squares of DA , AC ...
Página 40
... square of the whole line . Let the straight line AB be divided into any two parts in the point C the rectangle contained by AB , BC , together with the rectangle AB , AC , shall be equal to the square of AB . D FE Upon AB describe * the ...
... square of the whole line . Let the straight line AB be divided into any two parts in the point C the rectangle contained by AB , BC , together with the rectangle AB , AC , shall be equal to the square of AB . D FE Upon AB describe * the ...
Outras edições - Ver tudo
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.