The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 páginas |
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Página 13
... the direction CB . The change of direction which such a line must undergo in turning about C from the position CA into the position CB is called the angle ACB . 34. DEF . The angle contained by two straight lines ANGLES . 13 Angles.
... the direction CB . The change of direction which such a line must undergo in turning about C from the position CA into the position CB is called the angle ACB . 34. DEF . The angle contained by two straight lines ANGLES . 13 Angles.
Página 14
... turning about C which a line would go through in turning in the plane of ACB from the direction of CA to the direction of CB . 35. The angle between two straight lines has only to do with their directions , and therefore is quite ...
... turning about C which a line would go through in turning in the plane of ACB from the direction of CA to the direction of CB . 35. The angle between two straight lines has only to do with their directions , and therefore is quite ...
Página 16
... turning . For when the angle PQR coincides with ACB a straight line which turns about C from the direction CA into the direction CB , goes through the same amount of turning as a line which turns about Q from the direction QP into the ...
... turning . For when the angle PQR coincides with ACB a straight line which turns about C from the direction CA into the direction CB , goes through the same amount of turning as a line which turns about Q from the direction QP into the ...
Página 67
... turning about C , which a line would have to go through , in turning from the direction CA to that of CB , in the manner indicated by the dotted line . 89 . When any number of lines in one plane meet at a point , the angles at the point ...
... turning about C , which a line would have to go through , in turning from the direction CA to that of CB , in the manner indicated by the dotted line . 89 . When any number of lines in one plane meet at a point , the angles at the point ...
Página 117
... turning succes- sively about the points B , C , D , ... through the angles HBC , KCD , LDE , ... will be found on arriving again into the position AB , to have turned completely round through two straight angles . EXAMPLES XXXVII . 1 ...
... turning succes- sively about the points B , C , D , ... through the angles HBC , KCD , LDE , ... will be found on arriving again into the position AB , to have turned completely round through two straight angles . EXAMPLES XXXVII . 1 ...
Términos y frases comunes
ABC is equal adjacent angles alternate angles angle ABC angle ACB angle BAC angle equal angles FAB angular point area of ABC base BC bisectors bisects the angle centre coincide Consider the triangles Construction corresponding angle DEF are equal describe a triangle diagonal equal angles equal area equal in area equal respectively equal to BC equidistant equilateral triangle exterior angle finite straight line given angle given finite straight given parallelogram given point given straight line given triangle greater included angle interior opposite angle intersect isosceles triangle line BC middle point opposite sides perpendicular plane produced Prop Proposition Q.E.D. EXAMPLES quadrilateral radius rectilineal figure required to prove rhombus right angles right-angled triangle Shew side BC sides equal square straight angle surface third side triangle ABC triangle DEF triangles are equal Wherefore
Pasajes populares
Página 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 72 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Página 48 - 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 151 - 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 ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Página 118 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Página 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Página 114 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Página 125 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Página 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.