The Elements of Euclid: viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's Data |
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Page 11
... gle BFC is equal to the angle CGB , and the base BC is com- mon to the two triangles BFC , CGB ; wherefore these trian- gles are equalb , and their remaining angles , each to each , to which the equal sides are opposite ; therefore ...
... gle BFC is equal to the angle CGB , and the base BC is com- mon to the two triangles BFC , CGB ; wherefore these trian- gles are equalb , and their remaining angles , each to each , to which the equal sides are opposite ; therefore ...
Page 12
... gle EAF ; wherefore the given rectilineal angle BAC is bi- sected by the straight line AF . Which was to be done . PROP . X. PROB . To bisect a given finite straight line , that is , to di- vide it into two equal parts . Let AB be the ...
... gle EAF ; wherefore the given rectilineal angle BAC is bi- sected by the straight line AF . Which was to be done . PROP . X. PROB . To bisect a given finite straight line , that is , to di- vide it into two equal parts . Let AB be the ...
Page 18
... angle ABC would be equal a to the angle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it less ; because then the an- B b 18. 1. gle ABC would be less than A C the angle ACB ; but it is not : therefore 18 THE ELEMENTS.
... angle ABC would be equal a to the angle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it less ; because then the an- B b 18. 1. gle ABC would be less than A C the angle ACB ; but it is not : therefore 18 THE ELEMENTS.
Page 22
... gle EGF ; therefore CE G F the angle DFG is greater than EGF ; and much more is the angle EFG greater than the angle EGF ; and because the angle EFG of the triangle EFG is greater than its angle EGF , e 19. 1. and because the greatere ...
... gle EGF ; therefore CE G F the angle DFG is greater than EGF ; and much more is the angle EFG greater than the angle EGF ; and because the angle EFG of the triangle EFG is greater than its angle EGF , e 19. 1. and because the greatere ...
Page 26
... gles BGH , GHD upon the same side are together equal to two A G B right angles . For , if AGH be not equal to GHD , one of them must be great- C H D F er than the other ; let AGH be the greater ; and because the angle AGH is greater ...
... gles BGH , GHD upon the same side are together equal to two A G B right angles . For , if AGH be not equal to GHD , one of them must be great- C H D F er than the other ; let AGH be the greater ; and because the angle AGH is greater ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
altitude angle ABC angle BAC arch base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cosine 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 gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore
Popular passages
Page 95 - 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.
Page 153 - 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.
Page 306 - 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.
Page 11 - 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.
Page 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Page 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Page 26 - IF a straight line fall upon two parallel straight lines it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite, upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Page 11 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 93 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. VII. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.