The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 sider |
Inni boken
Resultat 1-5 av 38
Side 6
... lines and theoretical points . A Practical Diagram is the nearest approach we can make to a theoretical diagram by means of ... line can have any thickness . B A The above is a diagram representing a triangle , or three straight lines joining ...
... lines and theoretical points . A Practical Diagram is the nearest approach we can make to a theoretical diagram by means of ... line can have any thickness . B A The above is a diagram representing a triangle , or three straight lines joining ...
Side 10
... line passing through them is wholly in that surface . This definition does not tell us how to make a plane . It ... joining them lies wholly in that surface . For example a cylinder ; a cone . A plane is considered as unlimited in all ...
... line passing through them is wholly in that surface . This definition does not tell us how to make a plane . It ... joining them lies wholly in that surface . For example a cylinder ; a cone . A plane is considered as unlimited in all ...
Side 27
... line joining B to the middle point of AC is equal to half AC ; prove that the angle ABC is equal to the sum of the angles ACB , BAC . 4. The line AD which bisects the base BC of the isosceles triangle ABC also bisects the angle BAC . 5 ...
... line joining B to the middle point of AC is equal to half AC ; prove that the angle ABC is equal to the sum of the angles ACB , BAC . 4. The line AD which bisects the base BC of the isosceles triangle ABC also bisects the angle BAC . 5 ...
Side 32
... line BA , produced if necessary , such that BD is equal to CA ; Indicate the line joining D and C , as in the figure . Consider the triangles DBC , ACB ; because the two sides DB , BC and their included angle DBC in the triangle DBC ...
... line BA , produced if necessary , such that BD is equal to CA ; Indicate the line joining D and C , as in the figure . Consider the triangles DBC , ACB ; because the two sides DB , BC and their included angle DBC in the triangle DBC ...
Side 34
... line joining A and D , as in the figure . Consider the triangle BAD ; because the side BA is equal to the side BD ; therefore the angle BAD is equal to the angle BDA . [ Prop . 5. ] Now , the angle CDA is greater than its part BDA ...
... line joining A and D , as in the figure . Consider the triangle BAD ; because the side BA is equal to the side BD ; therefore the angle BAD is equal to the angle BDA . [ Prop . 5. ] Now , the angle CDA is greater than its part BDA ...
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.