Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson...together with a Selection of Geometrical Exercises from the Senate-house and College Examination Papers .... the first six books, and the portions of the eleventh and twelfth books read at CambridgeLongman, Green, Longman, Roberts, & Green, 1865 - 504 σελίδες |
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Αποτελέσματα 1 - 5 από τα 96.
Σελίδα 2
... vertex of the angle , that is , at the point in which the straight lines that contain the angle meet one another , is put between the other two letters , and one of these two is somewhere upon one of these straight lines , and the other ...
... vertex of the angle , that is , at the point in which the straight lines that contain the angle meet one another , is put between the other two letters , and one of these two is somewhere upon one of these straight lines , and the other ...
Σελίδα 11
... vertex of each of the triangles is without the other triangle . Because AC is equal to AD in the triangle ACD , therefore the angle ADC is equal to the angle ACD ; ( 1. 5. ) but the angle ACD is greater than the angle BCD ; ( ax . 9 ...
... vertex of each of the triangles is without the other triangle . Because AC is equal to AD in the triangle ACD , therefore the angle ADC is equal to the angle ACD ; ( 1. 5. ) but the angle ACD is greater than the angle BCD ; ( ax . 9 ...
Σελίδα 12
... vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base and on the same side of it , & c . Q. E. D. PROPOSITION VIII . THEOREM . If two triangles have two sides of the one equal to ...
... vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base and on the same side of it , & c . Q. E. D. PROPOSITION VIII . THEOREM . If two triangles have two sides of the one equal to ...
Σελίδα 29
... vertex of all the triangles , are equal to four right angles ; ( 1. 15. Cor . 2. ) therefore the same angles of these triangles are equal to the angles of the figure together with four right angles ; but it has been proved that the ...
... vertex of all the triangles , are equal to four right angles ; ( 1. 15. Cor . 2. ) therefore the same angles of these triangles are equal to the angles of the figure together with four right angles ; but it has been proved that the ...
Σελίδα 44
... vertex of the angle , and must not be confounded with the magnitude of the angle itself . The right angle is fixed in magnitude , and , on this account , it is made the standard with which all other angles are compared . Two straight ...
... vertex of the angle , and must not be confounded with the magnitude of the angle itself . The right angle is fixed in magnitude , and , on this account , it is made the standard with which all other angles are compared . Two straight ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ... Robert Potts Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ ABCD AC is equal angle ABC angle ACB angle BAC angle equal Apply Euc base BC bisects the angle chord circle ABC circle described circle whose center circles touch circumscribing circle construction describe a circle diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line greater hypotenuse isosceles triangle Let ABC line joining lines be drawn meet the circumference multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane point of contact polygon produced Prop proved Q.E.D. PROPOSITION quadrilateral quadrilateral figure radius rectangle contained rectilineal figure right angles right-angled triangle segment semicircle shew shewn similar triangles solid angle square on AC tangent THEOREM touch the circle triangle ABC vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 23 - 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 xiv - The sluggard is wiser in his own conceit than seven men that can render a reason.
Σελίδα 6 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Σελίδα 29 - 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 71 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Σελίδα 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Σελίδα 242 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 34 - Equal triangles, upon equal bases in the same straight line, and towards the same parts, are between the same parallels. Let the equal triangles ABC, DEF be upon equal bases BC, EF, in the same straight line BF, and towards the same parts.
Σελίδα 28 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.