The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 11.
Σελίδα 23
... equidistant from A and B. 11. A triangle ABC is turned over the line AC so as to have the new position AB'C ; prove that BB ' cuts AC in E so that the angles AEB , AEB ' are equal . 12. If the straight line which joins one angle of a ...
... equidistant from A and B. 11. A triangle ABC is turned over the line AC so as to have the new position AB'C ; prove that BB ' cuts AC in E so that the angles AEB , AEB ' are equal . 12. If the straight line which joins one angle of a ...
Σελίδα 33
... equidistant from A , B , C. 9. Prove the following construction for bisecting an angle BAC ; in AB take two points D , B , and let AC = AB and in AC take E so that AE = AD ; let BE , CD intersect in H ; then AH produced bisects the ...
... equidistant from A , B , C. 9. Prove the following construction for bisecting an angle BAC ; in AB take two points D , B , and let AC = AB and in AC take E so that AE = AD ; let BE , CD intersect in H ; then AH produced bisects the ...
Σελίδα 35
... equidistant from a given point in that line , prove that they cannot be equidistant from any other point in that line . 2. Two points C , D on opposite sides of a straight line AB are such that CA = DA , and CB = DB ; prove that the ...
... equidistant from a given point in that line , prove that they cannot be equidistant from any other point in that line . 2. Two points C , D on opposite sides of a straight line AB are such that CA = DA , and CB = DB ; prove that the ...
Σελίδα 51
... three bisectors of the angles of a triangle meet at one point . 7. Find the point in a given equilateral triangle which is equidistant from the angular points . Proposition 10 . 73. To bisect a given finite straight 4-2 PROPOSITION 9 . 51.
... three bisectors of the angles of a triangle meet at one point . 7. Find the point in a given equilateral triangle which is equidistant from the angular points . Proposition 10 . 73. To bisect a given finite straight 4-2 PROPOSITION 9 . 51.
Σελίδα 54
... FCE are equal , therefore each of the angles FCD , FCE is a right angle . [ Def . ] Wherefore , CF has been drawn from the point C at right angles to the line ACB . Q.E.F. Example . Find a series of points which are equidistant 54 EUCLID .
... FCE are equal , therefore each of the angles FCD , FCE is a right angle . [ Def . ] Wherefore , CF has been drawn from the point C at right angles to the line ACB . Q.E.F. Example . Find a series of points which are equidistant 54 EUCLID .
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Σελίδα 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.
Σελίδα 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 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.
Σελίδα 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.