The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
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Página 30
... reason , EF is equal to BC . Therefore AD is equal ( Ax . 1 ) to EF ; and DE is common to both . Wherefore the whole , or the re- mainder A E , is equal to the whole , or the remainder DF ( Ax . 2 or 3 ) ; and AB is equal ( I. 34 ) to ...
... reason , EF is equal to BC . Therefore AD is equal ( Ax . 1 ) to EF ; and DE is common to both . Wherefore the whole , or the re- mainder A E , is equal to the whole , or the remainder DF ( Ax . 2 or 3 ) ; and AB is equal ( I. 34 ) to ...
Página 35
... reason , the triangle KGC is equal to the triangle KFC . Therefore the two triangles A EK , KGC are equal ( Ax . 2 ) to the two triangles AHK , KFC . But the whole triangle ABC is equal to the whole triangle ADC . Therefore the ...
... reason , the triangle KGC is equal to the triangle KFC . Therefore the two triangles A EK , KGC are equal ( Ax . 2 ) to the two triangles AHK , KFC . But the whole triangle ABC is equal to the whole triangle ADC . Therefore the ...
Página 38
... reason , B A and A H are in the same straight line . Because the angle D B C is equal to the angle FB A , each of them being a right angle . To each of these equals , add the angle A B C. Therefore the whole angle DBA is equal ( Ax . 2 ) ...
... reason , B A and A H are in the same straight line . Because the angle D B C is equal to the angle FB A , each of them being a right angle . To each of these equals , add the angle A B C. Therefore the whole angle DBA is equal ( Ax . 2 ) ...
Página 43
... reason HF is a square , and it is described upon the side HG , which is ( I. 34 ) equal to AC . Therefore the figures HF and CK are the squares of AC and CB . Because the complement AG is equal ( I. 43 ) to the complement BOOK II . PROP ...
... reason HF is a square , and it is described upon the side HG , which is ( I. 34 ) equal to AC . Therefore the figures HF and CK are the squares of AC and CB . Because the complement AG is equal ( I. 43 ) to the complement BOOK II . PROP ...
Página 47
... reason , the rectangles PL and RF are equal . But the rectangle MP is ( I. 43 ) equal to the rectangle PL . Therefore the four rectangles AG , MP , PL , and RF are all equal . Because the four squares CK , BN , GR , and KO are four ...
... reason , the rectangles PL and RF are equal . But the rectangle MP is ( I. 43 ) equal to the rectangle PL . Therefore the four rectangles AG , MP , PL , and RF are all equal . Because the four squares CK , BN , GR , and KO are four ...
Otras ediciones - Ver todas
The Elements of geometry; or, The first six books, with the eleventh and ... Euclides Vista completa - 1881 |
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
A B C ABC is equal ABCD altitude angle ABC angle BAC base bisected Book centre circle circle ABC circumference common compounded cone Const contained Corollary cylinder definition demonstration described diameter divided double draw drawn equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half homologous inscribed join less magnitudes manner meet multiple opposite parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proposition proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar similarly solid solid angle sphere square Take taken THEOREM third touch triangle ABC vertex Wherefore whole
Pasajes populares
Página 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 42 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Página 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 130 - 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 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 143 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Página 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Página 115 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Página 45 - 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...