The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 Seiten |
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Seite 9
... less than that of AB , the point D will be between A and B ; and if the length of CD is greater than that of AB the point D will be beyond B. 22. It follows from the definition of Art . 17 that two straight lines cannot have more than ...
... less than that of AB , the point D will be between A and B ; and if the length of CD is greater than that of AB the point D will be beyond B. 22. It follows from the definition of Art . 17 that two straight lines cannot have more than ...
Seite 16
... ' . B R P 40. When an angle ACB is less than PQR , as in the above figure , then if the angle PQR is applied to ACB it will take up a position like that indicated by P'CR ' . SECTION III . EQUALITY OF TRIANGLES . Triangles . 41. 16 EUCLID .
... ' . B R P 40. When an angle ACB is less than PQR , as in the above figure , then if the angle PQR is applied to ACB it will take up a position like that indicated by P'CR ' . SECTION III . EQUALITY OF TRIANGLES . Triangles . 41. 16 EUCLID .
Seite 41
... less than AC ; produce AB to D so that it shall be equal to AC . 4. AB is a given straight line ; shew how to produce AB to C so that AC shall be ( i ) twice , ( ii ) three times AB . 5. AB and AC are two given straight lines ; cut off ...
... less than AC ; produce AB to D so that it shall be equal to AC . 4. AB is a given straight line ; shew how to produce AB to C so that AC shall be ( i ) twice , ( ii ) three times AB . 5. AB and AC are two given straight lines ; cut off ...
Seite 44
... less . 4. From the line of which AB is a finite portion cut off a part twice as long as a given straight line AC . 5. Cut off a part from AB in Question 4 three times as long as AC . 6. ABC is an unlimited straight line ; shew how to ...
... less . 4. From the line of which AB is a finite portion cut off a part twice as long as a given straight line AC . 5. Cut off a part from AB in Question 4 three times as long as AC . 6. ABC is an unlimited straight line ; shew how to ...
Seite 47
... greater than the other ; but that when AB is less than twice BC either circle may be the greater according to the way in which the figure is drawn . Proposition 3 . 71. From the greater of two given PROPOSITION 2 . 47.
... greater than the other ; but that when AB is less than twice BC either circle may be the greater according to the way in which the figure is drawn . Proposition 3 . 71. From the greater of two given PROPOSITION 2 . 47.
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.