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 ... |
From inside the book
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Page vi
... taken , the straight line between them , with its prolongation either way , may be proved to lie wholly in that surface . A surface of this kind is called a plane . From these , all the relations of straight lines and planes may be ...
... taken , the straight line between them , with its prolongation either way , may be proved to lie wholly in that surface . A surface of this kind is called a plane . From these , all the relations of straight lines and planes may be ...
Page xii
... taken in some part of a line which is not the extremity , it may be imagined to be determined by causing the line to terminate at that point . See Note . VIII . Anything that has boundaries which are fixed , is called a figure . Figures ...
... taken in some part of a line which is not the extremity , it may be imagined to be determined by causing the line to terminate at that point . See Note . VIII . Anything that has boundaries which are fixed , is called a figure . Figures ...
Page 2
... taken from the first , the remainder is equal to the second . And a magnitude is said to be less than another by a certain mag- nitude , when this last - mentioned magnitude being added to the first , the sum is equal to the second ...
... taken from the first , the remainder is equal to the second . And a magnitude is said to be less than another by a certain mag- nitude , when this last - mentioned magnitude being added to the first , the sum is equal to the second ...
Page 4
... taken in his compasses in order to describe the head that would fit . But he does not know the reasons why this will necessarily be the case , not only in the instances which he has tried , but in all which he has not tried also . And ...
... taken in his compasses in order to describe the head that would fit . But he does not know the reasons why this will necessarily be the case , not only in the instances which he has tried , but in all which he has not tried also . And ...
Page 5
... taken together , amount to the establishment of the universal proposition . XXX . What is called the converse of a proposition is , when the premises and the conclusion are made to change places , and the proposition so arising is ...
... taken together , amount to the establishment of the universal proposition . XXX . What is called the converse of a proposition is , when the premises and the conclusion are made to change places , and the proposition so arising is ...
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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.