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 ...Robert Heward, 1833 - 150 páginas |
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Página vi
... magnitude and the other to decrease , the line described by their point of contact will be without change of place throughout ; such a line is called a straight line . If two equal spheres be placed touching one another externally , and ...
... magnitude and the other to decrease , the line described by their point of contact will be without change of place throughout ; such a line is called a straight line . If two equal spheres be placed touching one another externally , and ...
Página 1
... 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 divided into ...
... 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 divided into ...
Página 2
... magnitude is said to be greater than another by a certain magnitude , when this last - mentioned magnitude being taken from the first , the remainder is equal to the second . And a magnitude is said to be less than another by a certain ...
... magnitude is said to be greater than another by a certain magnitude , when this last - mentioned magnitude being taken from the first , the remainder is equal to the second . And a magnitude is said to be less than another by a certain ...
Página 3
... magnitude has been cut off equal to another magnitude ; these two magnitudes may at any time afterwards be avouched to be equal by construction . For one of them has been specially constituted and constructed equal to the other . XXIV ...
... magnitude has been cut off equal to another magnitude ; these two magnitudes may at any time afterwards be avouched to be equal by construction . For one of them has been specially constituted and constructed equal to the other . XXIV ...
Página 5
... magnitudes which are equal to the same , are equal to one another ; the converse of this proposition is , that magnitudes which are equal to one another , are equal to the same . XXXI . What is called the negative of a proposition is ...
... magnitudes which are equal to the same , are equal to one another ; the converse of this proposition is , that magnitudes which are equal to one another , are equal to the same . XXXI . What is called the negative of a proposition is ...
Otras ediciones - Ver todas
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Página 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 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.
Página 72 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 103 - ... twice as many right angles as the figure has sides.
Página 70 - Any two angles of a triangle are together less than two right angles.
Página 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.
Página 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.