The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 σελίδες |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 35
... exterior angles EAD , FDA are equal . [ Prop . 5. Cor . ] But the angle EAD is greater than its part DAC ; therefore also the angle FDA is greater than DAC . Again the angle CDA is greater than its part FDA ; still more therefore is the ...
... exterior angles EAD , FDA are equal . [ Prop . 5. Cor . ] But the angle EAD is greater than its part DAC ; therefore also the angle FDA is greater than DAC . Again the angle CDA is greater than its part FDA ; still more therefore is the ...
Σελίδα 76
... exterior angle is greater than either of the interior opposite angles . Let a side BC of the triangle ABC be produced to D ; it is required to prove that the angle ACD is greater than either the angle BAC or the angle ABC . F E B C Let ...
... exterior angle is greater than either of the interior opposite angles . Let a side BC of the triangle ABC be produced to D ; it is required to prove that the angle ACD is greater than either the angle BAC or the angle ABC . F E B C Let ...
Σελίδα 77
... angle BCG is greater than the corresponding interior angle ABC . But ACD and BCG , being vertically opposite angles ... exterior angle and the other an interior opposite angle of the triangle GBE in which case the angles ABC , DEF are ...
... angle BCG is greater than the corresponding interior angle ABC . But ACD and BCG , being vertically opposite angles ... exterior angle and the other an interior opposite angle of the triangle GBE in which case the angles ABC , DEF are ...
Σελίδα 78
... exterior angle of a triangle greater than the interior adjacent angle ? 2. From a given point A a perpendicular AD is drawn to a given straight line BDC ; prove that if any point K be taken in BC the angle AKD is an acute angle . 3 ...
... exterior angle of a triangle greater than the interior adjacent angle ? 2. From a given point A a perpendicular AD is drawn to a given straight line BDC ; prove that if any point K be taken in BC the angle AKD is an acute angle . 3 ...
Σελίδα 79
... angles . Let ABC be a triangle ; it is required to prove that any two of its angles are together less than two right angles . B Let D be a point on one of the sides BC produced ; then , because ACD is an exterior angle of the triangle ...
... angles . Let ABC be a triangle ; it is required to prove that any two of its angles are together less than two right angles . B Let D be a point on one of the sides BC produced ; then , because ACD is an exterior angle of the triangle ...
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.