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 51
... perpendicular to it ; and is also said to be at right angles to it . XXXVIII . An angle greater than a right angle , is called obtuse . XXXIX . acute . An angle less than a right angle , is called XL . Angles greater or less than right ...
... perpendicular to it ; and is also said to be at right angles to it . XXXVIII . An angle greater than a right angle , is called obtuse . XXXIX . acute . An angle less than a right angle , is called XL . Angles greater or less than right ...
Page 52
... perpendicular . XLIX . A triangle which has an obtuse angle , is called obtuse - angled . L. A triangle which has all its angles acute , is called acule - angled . LI . A triangle which has all its angles oblique , is called oblique ...
... perpendicular . XLIX . A triangle which has an obtuse angle , is called obtuse - angled . L. A triangle which has all its angles acute , is called acule - angled . LI . A triangle which has all its angles oblique , is called oblique ...
Page 68
... perpendicular to BAC and bisect the angle BAC by dividing it into two right angles . Third Case ; if the angle BAC is greater than the sum of two right angles ( or the angle intended is that formed by the turning of the radius vectus ...
... perpendicular to BAC and bisect the angle BAC by dividing it into two right angles . Third Case ; if the angle BAC is greater than the sum of two right angles ( or the angle intended is that formed by the turning of the radius vectus ...
Page 76
... perpendicular to an as- signed straight line of unlimited length , from an assigned point without it . Let AB be the ... perpendicular to AB . In AB take any point , as D ; and join CD . If CDB is a right angle , then there is drawn a ...
... perpendicular to an as- signed straight line of unlimited length , from an assigned point without it . Let AB be the ... perpendicular to AB . In AB take any point , as D ; and join CD . If CDB is a right angle , then there is drawn a ...
Page 77
... perpendicular to the other ; the perpendicular shall fall on that side of C , on which is the acute angle . C D 77 For the perpendicular cannot fall upon the point C ; because ACD is not a right angle but an acute angle . Neither can it ...
... perpendicular to the other ; the perpendicular shall fall on that side of C , on which is the acute angle . C D 77 For the perpendicular cannot fall upon the point C ; because ACD is not a right angle but an acute angle . Neither can it ...
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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.