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 Seiten |
Im Buch
Ergebnisse 1-5 von 19
Seite vii
... formed into an Intercalary Book , with a view to facilitate their postponement in the case of students beginning geometry for the first time . And for the further convenience of this class , a Reca- pitulation of the principal contents ...
... formed into an Intercalary Book , with a view to facilitate their postponement in the case of students beginning geometry for the first time . And for the further convenience of this class , a Reca- pitulation of the principal contents ...
Seite ix
... formed by the junction of two sides , keeping ever at right angles to it , cannot cease to cut the bases and make ... forming one straight line as must be the case if the angles opposite to the bases in the tesseras were right angles ...
... formed by the junction of two sides , keeping ever at right angles to it , cannot cease to cut the bases and make ... forming one straight line as must be the case if the angles opposite to the bases in the tesseras were right angles ...
Seite 14
... formed by the substance out of which + 1.Nom.14 . it may be supposed to be taken , are reciprocalst . + Constr . For their boundaries are in contact in every part at once . COR . 4. The surfaces of concentric spheres either coincide ...
... formed by the substance out of which + 1.Nom.14 . it may be supposed to be taken , are reciprocalst . + Constr . For their boundaries are in contact in every part at once . COR . 4. The surfaces of concentric spheres either coincide ...
Seite 23
... formed through the scraping away of the greatest possible quantity of matter by the turning of the sphere A in different directions about B. ] Let then this sphere , which has none other of the concentric spheres within it , be the ...
... formed through the scraping away of the greatest possible quantity of matter by the turning of the sphere A in different directions about B. ] Let then this sphere , which has none other of the concentric spheres within it , be the ...
Seite 36
... formed a three - sided figure ; and no point in any one side , shall coincide with any point in either of the other sides , except the points which were joined . For if any points other than these , should coincide ; the whole of the ...
... formed a three - sided figure ; and no point in any one side , shall coincide with any point in either of the other sides , except the points which were joined . For if any points other than these , should coincide ; the whole of the ...
Andere Ausgaben - Alle anzeigen
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Seite 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Seite 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.
Seite 72 - Any two sides of a triangle are together greater than the third side.
Seite 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.
Seite 103 - ... twice as many right angles as the figure has sides.
Seite 70 - Any two angles of a triangle are together less than two right angles.
Seite 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.
Seite 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.