Elements of Geometry: Being Chiefly a Selection from Playfair's GeometryA. Walker, 1829 - 186 páginas |
Dentro del libro
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Página 40
... perp . to EF , the angles at E and F will be right angles ( 10 Def . ) , and therefore equal ( 11 Def . Cor . ) ; where- fore AB is parallel to CD . A E ED . B PROPOSITION XXIX . THEOREM . C F If a straight line intersect two parallel ...
... perp . to EF , the angles at E and F will be right angles ( 10 Def . ) , and therefore equal ( 11 Def . Cor . ) ; where- fore AB is parallel to CD . A E ED . B PROPOSITION XXIX . THEOREM . C F If a straight line intersect two parallel ...
Página 41
... perp . to CD . Therefore AEF and BEF C are right angles , therefore EF is per- pendicular to AB . ED . E B F D PROPOSITION XXX . THEOREM . Straight lines which are parallel to the same straight line are parallel to one another . Ꮐ Let ...
... perp . to CD . Therefore AEF and BEF C are right angles , therefore EF is per- pendicular to AB . ED . E B F D PROPOSITION XXX . THEOREM . Straight lines which are parallel to the same straight line are parallel to one another . Ꮐ Let ...
Página 50
... perp . to AB , and make AD equal to AB ; through D draw DE parallel to AB ( Prop . 31 ) , and through B draw BE parallel to AD ; then ADEB is a square described on AB . For ADEB is a paral . , therefore AB is equal to DE ( Prop . 34 ) ...
... perp . to AB , and make AD equal to AB ; through D draw DE parallel to AB ( Prop . 31 ) , and through B draw BE parallel to AD ; then ADEB is a square described on AB . For ADEB is a paral . , therefore AB is equal to DE ( Prop . 34 ) ...
Página 51
... perp . to EF ; AB is less than AC , and AC is less than AD . For since B is a right angle , ACB is an acute angle ( 3 Cor . 32 ) , E- therefore the side AC is greater than AB ( Prop . 19 ) . D A -F B Again , because ACB is an acute ...
... perp . to EF ; AB is less than AC , and AC is less than AD . For since B is a right angle , ACB is an acute angle ( 3 Cor . 32 ) , E- therefore the side AC is greater than AB ( Prop . 19 ) . D A -F B Again , because ACB is an acute ...
Página 61
... parallel straight lines AB , CD , has the same inclina- tion to both , that is , it makes the external angle C EGB equal to the internal H D angle EHD on the same side of it . F If EF be perp . to one AB , it GEOMETRY BOOK I. 61.
... parallel straight lines AB , CD , has the same inclina- tion to both , that is , it makes the external angle C EGB equal to the internal H D angle EHD on the same side of it . F If EF be perp . to one AB , it GEOMETRY BOOK I. 61.
Otras ediciones - Ver todas
Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair Sin vista previa disponible - 2023 |
Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair Sin vista previa disponible - 2023 |
Términos y frases comunes
ABC is equal ABCD alternate angles angle ABC angle ACB angle BAC angles AGH angles equal base ABC bases and altitudes bisect centre chord circumference cone Consequently cylinder demonstrations described diagonals diameter divided draw equal angles equal arches equal bases equal circles equal to AC equiangular Euclid's Euclid's Elements exterior angle fore four quantities four right angles geometry given point given straight line gles greater Hence homologous sides intersect KLMN Let ABC meet opposite angles opposite side paral parallel lines parallel to CD parallelogram parallelopipeds perp perpendicular plane polygon prism Prop pyramid Q. E. D. COR Q. E. D. PROPOSITION radius rectangle contained right angled triangle Scholium segments semicircle side AC similar similar triangles solid square straight line &c subtended tangent THEOREM triangle ABC vertex wherefore
Pasajes populares
Página 36 - Any two sides of a triangle are together greater than the third side.
Página 80 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Página 42 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...
Página 30 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Página 20 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 38 - Problem. At a given point in a given straight line to make a rectilineal angle equal to a given rectilineal angle.
Página 113 - Wherefore also the angle BAD is equal to the angle CAD : Therefore the angle BAC is cut into two equal angles by the straight line AD.
Página 24 - DE ; the point B shall coincide with the point E, because AB is equal to DE; and AB coinciding with DE, AC shall coincide...
Página 36 - The greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.