Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ... |
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Page 108
... square . NOм . 3. A rectangle of which only the opposite sides are equal , is called an oblong . NOм . 4. A parallelogram of which all the sides are equal , but the angles aret not right angles , is called a rhombus . Noм . 5. A ...
... square . NOм . 3. A rectangle of which only the opposite sides are equal , is called an oblong . NOм . 4. A parallelogram of which all the sides are equal , but the angles aret not right angles , is called a rhombus . Noм . 5. A ...
Page 116
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon it . D C + I . 10 . +1.3 . + Constr . 11.34 . From the points A and B , draw † AD and BC at right angles to AB and on the ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon it . D C + I . 10 . +1.3 . + Constr . 11.34 . From the points A and B , draw † AD and BC at right angles to AB and on the ...
Page 117
... square , is equal to the side EF of the other square . NN KB E For if AB be not equal to EF , one of them must be the greater . Let AB be the greater ; and make ‡ AK and AI each equal to EF ; and join KI . Join also BD , FH . Because AK ...
... square , is equal to the side EF of the other square . NN KB E For if AB be not equal to EF , one of them must be the greater . Let AB be the greater ; and make ‡ AK and AI each equal to EF ; and join KI . Join also BD , FH . Because AK ...
Page 118
... square described upon a greater straight line , is greater than the square described upon a less . H Let the straight line AB be greater . D C than the straight line EF . The square ABCD which is described upon AB , is greater than the ...
... square described upon a greater straight line , is greater than the square described upon a less . H Let the straight line AB be greater . D C than the straight line EF . The square ABCD which is described upon AB , is greater than the ...
Page 119
... square described on the side which is opposite to the right angle , is equal to the sum of the squares described on the sides between which is the right angle . Let ABC be a triangle having the right angle BAC . The square described on ...
... square described on the side which is opposite to the right angle , is equal to the sum of the squares described on the sides between which is the right angle . Let ABC be a triangle having the right angle BAC . The square described on ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson No preview available - 2015 |
Common terms and phrases
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angular points assigned point Axiom axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal angles equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater half the angle hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively SCHOLIUM self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.-If third side triangle ABC turned unlimited length Wherefore
Popular passages
Page 51 - 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.
Page 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Page 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Page 72 - Any two sides of a triangle are together greater than the third side.
Page 55 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Page 103 - ... twice as many right angles as the figure has sides.
Page 70 - Any two angles of a triangle are together less than two right angles.
Page 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.
Page 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.