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 vi
... called a sphere . A sphere may be turned in any manner whatsoever about its centre , without change of place . Consequences deducible from this are , that if two spheres touch one another externally , they touch only in a point ; and if ...
... called a sphere . A sphere may be turned in any manner whatsoever about its centre , without change of place . Consequences deducible from this are , that if two spheres touch one another externally , they touch only in a point ; and if ...
Page ix
... called the base ] has the angles at the base less than right angles , the angles opposite to the base cannot be right angles . And this because , if a number of such figures are placed side by side , a straight line of unlimited length ...
... called the base ] has the angles at the base less than right angles , the angles opposite to the base cannot be right angles . And this because , if a number of such figures are placed side by side , a straight line of unlimited length ...
Page xi
... called its name . The giving of names for the purposes of science , is called Nomenclature . Anything that can be made the object of touch , is called a body . III . A body whose particles are immoveable among themselves , at least by ...
... called its name . The giving of names for the purposes of science , is called Nomenclature . Anything that can be made the object of touch , is called a body . III . A body whose particles are immoveable among themselves , at least by ...
Page xii
... called a line . VII . A line , consequently , has length , but not thickness or breadth . For the surface itself has no thickness ; wherefore its boundary can have none . And if the so - called boundary had breadth , it would not be the ...
... called a line . VII . A line , consequently , has length , but not thickness or breadth . For the surface itself has no thickness ; wherefore its boundary can have none . And if the so - called boundary had breadth , it would not be the ...
Page 1
... called magnitudes . XIV . Magnitudes which if their boundaries were applied to one another , would coincide ; or might be made capable of doing so , by a different arrangement of parts ; are called equal . Equal magnitudes may be ...
... called magnitudes . XIV . Magnitudes which if their boundaries were applied to one another , would coincide ; or might be made capable of doing so , by a different arrangement of parts ; are called equal . Equal magnitudes may be ...
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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.