The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 sider |
Inni boken
Resultat 1-5 av 60
Side
... 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 , equal in all respects to ABC , can exist ...
... 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 , equal in all respects to ABC , can exist ...
Side 17
... triangle has three angles . Hence its name . The angles of the triangle ABC are CAB , BCA , ABC . The points A , B , C are called the angular points of the triangle ABC . A triangle encloses a certain amount of surface called its area .
... triangle has three angles . Hence its name . The angles of the triangle ABC are CAB , BCA , ABC . The points A , B , C are called the angular points of the triangle ABC . A triangle encloses a certain amount of surface called its area .
Side 19
... triangle . B A Thus when the triangles ABC , DEF are equal in all respects then AB = DE , AC = DF , BC = EF ; the ... triangles have two sides 2-2 EQUAL TRIANGLES . 19.
... triangle . B A Thus when the triangles ABC , DEF are equal in all respects then AB = DE , AC = DF , BC = EF ; the ... triangles have two sides 2-2 EQUAL TRIANGLES . 19.
Side 20
... ABC , DEF represent two triangles , in which AB is equal to DE , AC 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 ... triangle ABC coincides with 20 EUCLID .
... ABC , DEF represent two triangles , in which AB is equal to DE , AC 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 ... triangle ABC coincides with 20 EUCLID .
Side 21
... triangles ABC , DEF of Prop . 4 , the sides AB , AC , DE , DF are produced to H , K , L , M respectively , then the angle HBC is equal to the angle LEF and the angle KCB to the angle MFE . H / K M For the triangle ABC coinciding with ...
... triangles ABC , DEF of Prop . 4 , the sides AB , AC , DE , DF are produced to H , K , L , M respectively , then the angle HBC is equal to the angle LEF and the angle KCB to the angle MFE . H / K M For the triangle ABC coinciding with ...
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.