The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 53
... perpendicular to it . Thus in the above figure , CD is perpendicular to ACB . Also the lines ACB and DC are said to be at right angles to each other . Proposition 11 . 76. To draw a straight line at PROPOSITION 10 . 53.
... perpendicular to it . Thus in the above figure , CD is perpendicular to ACB . Also the lines ACB and DC are said to be at right angles to each other . Proposition 11 . 76. To draw a straight line at PROPOSITION 10 . 53.
Σελίδα 55
... perpendicular to AB . Hence we have the following ] A B Construction . Bisect AB in D and draw DE at right angles to AB ; in DE take any point C , then C is a point equidistant from A and B. Proof . Consider the triangles ADC , BDC ...
... perpendicular to AB . Hence we have the following ] A B Construction . Bisect AB in D and draw DE at right angles to AB ; in DE take any point C , then C is a point equidistant from A and B. Proof . Consider the triangles ADC , BDC ...
Σελίδα 57
... perpendicular from the vertex on the base is equal to a given finite straight line EF and cuts the base in a given point D. 6. Describe an isosceles triangle when the length of the base and of the perpendicular from the vertex to the ...
... perpendicular from the vertex on the base is equal to a given finite straight line EF and cuts the base in a given point D. 6. Describe an isosceles triangle when the length of the base and of the perpendicular from the vertex to the ...
Σελίδα 58
... perpendicular to a given straight line from a given point without it . Let AB be the given straight line and C the given point ; it is required to draw from C a straight line which shall be perpendicular to AB . A Construction . E On ...
... perpendicular to a given straight line from a given point without it . Let AB be the given straight line and C the given point ; it is required to draw from C a straight line which shall be perpendicular to AB . A Construction . E On ...
Σελίδα 59
... perpendicular to the base the triangle is isosceles . 5. State and prove the converse of Question 4 . 6. Prove that the diagonals of a rhombus are at right angles to each other . [ A rhombus is an equilateral figure having four sides ...
... perpendicular to the base the triangle is isosceles . 5. State and prove the converse of Question 4 . 6. Prove that the diagonals of a rhombus are at right angles to each other . [ A rhombus is an equilateral figure having four sides ...
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.