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 7
... unequal . And that sum is greatest , in which the unequal was greatest . For , of the unequals , one is greatest ; that is , it is equal to the other and a certain magnitude besides . But if to the equals were added equals , the sums ...
... unequal . And that sum is greatest , in which the unequal was greatest . For , of the unequals , one is greatest ; that is , it is equal to the other and a certain magnitude besides . But if to the equals were added equals , the sums ...
Página 8
... unequal . And that remainder is greatest , in which the unequal was greatest . For , of the unequals , one is equal to the other and a certain magnitude besides . But if the equals were taken from equals , the remainders ( by Cor . 7 ) ...
... unequal . And that remainder is greatest , in which the unequal was greatest . For , of the unequals , one is equal to the other and a certain magnitude besides . But if the equals were taken from equals , the remainders ( by Cor . 7 ) ...
Página 10
... unequal magnitudes , and from the double of the greater be taken the double of the less ; the re- mainder is double of the difference of the magnitudes . And so of any other equimultiples . Let A and B be two magnitudes ; of which A is ...
... unequal magnitudes , and from the double of the greater be taken the double of the less ; the re- mainder is double of the difference of the magnitudes . And so of any other equimultiples . Let A and B be two magnitudes ; of which A is ...
Página 15
... unequal ; wherefore , if their centres be applied to- gether , their surfaces ( by Cor . 5 ) will not coincide at all , but one + 1.Nom.15 . be interior to the other ; that is to say , one sphere will be greater + than the other ; which ...
... unequal ; wherefore , if their centres be applied to- gether , their surfaces ( by Cor . 5 ) will not coincide at all , but one + 1.Nom.15 . be interior to the other ; that is to say , one sphere will be greater + than the other ; which ...
Página 46
... unequal . And that sum is greatest , in which the unequal was greatest . If equals be taken from equals , the remainders are equal . If equals be taken from unequals , the remainders are unequal . And that remainder is greatest , in ...
... unequal . And that sum is greatest , in which the unequal was greatest . If equals be taken from equals , the remainders are equal . If equals be taken from unequals , the remainders are unequal . And that remainder is greatest , in ...
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.