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 ix
... 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 which shall ...
... 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 which shall ...
Página 52
... base and 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 ...
... base and 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 ...
Página 84
... base ] , two straight lines equal to one another be drawn towards the same side , making equal interior angles at the base , each less than the sum of two right angles , but the two equal straight lines do not meet ; and the extremities ...
... base ] , two straight lines equal to one another be drawn towards the same side , making equal interior angles at the base , each less than the sum of two right angles , but the two equal straight lines do not meet ; and the extremities ...
Página 86
... base , is bisected at right angles by the perpendicular drawn from the middle of the base ; and is parallel to the base . For it has been shown that EF bisects DC at right angles . Wherefore , because EFC is a right angle , and AEF also ...
... base , is bisected at right angles by the perpendicular drawn from the middle of the base ; and is parallel to the base . For it has been shown that EF bisects DC at right angles . Wherefore , because EFC is a right angle , and AEF also ...
Página 88
... base AC are drawn * two equal straight lines AB , CE , making with AC the equal angles CAB , ACE , each of which is less than the sum of two right angles ; BACE is a tessera , and the angles ABE , CEB are equal to one another . And ...
... base AC are drawn * two equal straight lines AB , CE , making with AC the equal angles CAB , ACE , each of which is less than the sum of two right angles ; BACE is a tessera , and the angles ABE , CEB are equal to one another . And ...
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.