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 |
Dentro del libro
Página 1
... same place , are said to coincide . The only way in which coincidence can actually be brought to pass , is when the things touch one another ... equal to the distance of C and D ; when if A and C were applied to one another , B and D might ...
... same place , are said to coincide . The only way in which coincidence can actually be brought to pass , is when the things touch one another ... equal to the distance of C and D ; when if A and C were applied to one another , B and D might ...
Página 8
... one remainder is greater than the other . Add each to the equals that were ... things by the hypothesis were equal to begin with . The assumption ... same , or the same from equals . COR . 8. If equals be taken from unequals , the ...
... one remainder is greater than the other . Add each to the equals that were ... things by the hypothesis were equal to begin with . The assumption ... same , or the same from equals . COR . 8. If equals be taken from unequals , the ...
Página 53
... equal to AB . And because the point B is the centre of the circle ACE , and C and A are points in the circumference ... things which are equal to the * INTERC . 1. same , are * equal to one another ; therefore AC is equal to BC ...
... equal to AB . And because the point B is the centre of the circle ACE , and C and A are points in the circumference ... things which are equal to the * INTERC . 1. same , are * equal to one another ; therefore AC is equal to BC ...
Página 54
... equal to BC . From the point A to B draw * the straight line AB , and upon it describet the equilateral triangle K H E INTERC . 12. DAB , and prolong the straight lines DA and DB , to E and F ; which will be in the same ... things which are * ...
... equal to BC . From the point A to B draw * the straight line AB , and upon it describet the equilateral triangle K H E INTERC . 12. DAB , and prolong the straight lines DA and DB , to E and F ; which will be in the same ... things which are * ...
Página 119
... equal to the sum of the squares described on the sides between which is the ... same manner AL and CE are parallel . Wherefore AL lies between BD and CE ... things are ‡ equal to one another ; therefore the parallel- ogram BL is equal to ...
... equal to the sum of the squares described on the sides between which is the ... same manner AL and CE are parallel . Wherefore AL lies between BD and CE ... things are ‡ equal to one another ; therefore the parallel- ogram BL is equal to ...
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.