The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 Seiten |
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Ergebnisse 1-5 von 22
Seite 29
... meets BC in D ; prove that if the angles ADB , ADC are equal the triangle ABC is isosceles . 4. In an isosceles triangle ABC the equal angles are bisected by the lines BD , CE which meet the opposite sides in D and E respectively ...
... meets BC in D ; prove that if the angles ADB , ADC are equal the triangle ABC is isosceles . 4. In an isosceles triangle ABC the equal angles are bisected by the lines BD , CE which meet the opposite sides in D and E respectively ...
Seite 46
... meet this circle in E. With centre D and radius DE describe the circle EGH . Produce the straight line DA to meet this circle in G. Then AG is a line such as is required . Proof . Because BE and BC are radii of the circle ECF ...
... meet this circle in E. With centre D and radius DE describe the circle EGH . Produce the straight line DA to meet this circle in G. Then AG is a line such as is required . Proof . Because BE and BC are radii of the circle ECF ...
Seite 51
... 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.
... 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.
Seite 67
... meet at a point , the angles at the point altogether make up four right angles . K E F B Α For let CA , CB , CD , CE , CF be any number of lines all drawn from the point C. Produce any one of the lines AC through C to K. Then the angles ...
... meet at a point , the angles at the point altogether make up four right angles . K E F B Α For let CA , CB , CD , CE , CF be any number of lines all drawn from the point C. Produce any one of the lines AC through C to K. Then the angles ...
Seite 69
... meet the bisector of the angle B in the same point . 8. In the figure of Question 7 , prove that the perpendicular to BC drawn from D meets the bisectors of the angles at B and C in the same point . 9. Deduce from the results of ...
... meet the bisector of the angle B in the same point . 8. In the figure of Question 7 , prove that the perpendicular to BC drawn from D meets the bisectors of the angles at B and C in the same point . 9. Deduce from the results of ...
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Seite 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.
Seite 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Seite 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.
Seite 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.