The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 sider |
Inni boken
Resultat 1-5 av 89
Side
... angle . If there is a line which divides the angle ABC into two equal parts , it must cut the line AC in some point E ; and then by Prop . 4 the triangles ABE , CBE are equal in all respects . Similarly we may assume that a triangle DEF , ...
... angle . If there is a line which divides the angle ABC into two equal parts , it must cut the line AC in some point E ; and then by Prop . 4 the triangles ABE , CBE are equal in all respects . Similarly we may assume that a triangle DEF , ...
Side 18
... triangle , the third side , i.e. the one which is unequal to the others , is called the base . Also the vertex of an isosceles triangle is the angular point which is opposite the base . 47. When two triangles are said to be equal in 18 ...
... triangle , the third side , i.e. the one which is unequal to the others , is called the base . Also the vertex of an isosceles triangle is the angular point which is opposite the base . 47. When two triangles are said to be equal in 18 ...
Side 19
Arranged for Beginners Euclid, John Bascombe Lock. 47. When two triangles are said to be equal in all respects , it is meant that each part of one triangle is equal to the corresponding part of the other triangle . B A Thus when the ...
Arranged for Beginners Euclid, John Bascombe Lock. 47. When two triangles are said to be equal in all respects , it is meant that each part of one triangle is equal to the corresponding part of the other triangle . B A Thus when the ...
Side 20
... equal to DF , and the angle BAC equal to the angle EDF ; it is required to prove that the triangles represented by ABC , DEF are equal in all respects . B Let the triangle ABC be applied to the triangle DEF so that the point A is on the ...
... equal to DF , and the angle BAC equal to the angle EDF ; it is required to prove that the triangles represented by ABC , DEF are equal in all respects . B Let the triangle ABC be applied to the triangle DEF so that the point A is on the ...
Side 21
... triangle DEF and is therefore equal to it . Wherefore , if two triangles have two sides , etc. Q.E.D. 50. Corollary . If in the triangles ABC , DEF of Prop . 4 , the sides AB , AC , DE , DF are produced to H , K , L , M respectively ...
... triangle DEF and is therefore equal to it . Wherefore , if two triangles have two sides , etc. Q.E.D. 50. Corollary . If in the triangles ABC , DEF of Prop . 4 , the sides AB , AC , DE , DF are produced to H , K , L , M respectively ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Side 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.
Side 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 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.
Side 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.