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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Σελίδα 25
... produced will meet , either towards A and C , or towards B and D. Let AB , CD , be produced and meet if possible , towards Band D , in the point G ; then GEF is a triangle . And because a side GE of the triangle GEF is produced to A ...
... produced will meet , either towards A and C , or towards B and D. Let AB , CD , be produced and meet if possible , towards Band D , in the point G ; then GEF is a triangle . And because a side GE of the triangle GEF is produced to A ...
Σελίδα 28
... produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles . Let ABC be a triangle , and let one of its sides BC be produced to ...
... produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles . Let ABC be a triangle , and let one of its sides BC be produced to ...
Σελίδα 36
... produced ; let them be produced and meet in K , through K draw KL parallel to EA or FH , and produce HA , GB to meet KL in the points L , M. Then HLKF is a parallelogram , of which the diameter is IIK ; and AG , ME are the ...
... produced ; let them be produced and meet in K , through K draw KL parallel to EA or FH , and produce HA , GB to meet KL in the points L , M. Then HLKF is a parallelogram , of which the diameter is IIK ; and AG , ME are the ...
Σελίδα 52
... producing DA to meet the cir- cumference in L. By a similar construction the less of two given straight lines may be produced , so that the less together with the part produced may be equal to the greater . Prop . 111. This problem ...
... producing DA to meet the cir- cumference in L. By a similar construction the less of two given straight lines may be produced , so that the less together with the part produced may be equal to the greater . Prop . 111. This problem ...
Σελίδα 54
... produced in the fig .. Prop . IX , it bisects the angle which is the defect of the angle BAC from four right angles . By means of this problem , any angle may be divided into four , eight , sixteen , & c . equal angles .. • Prop . x . A ...
... produced in the fig .. Prop . IX , it bisects the angle which is the defect of the angle BAC from four right angles . By means of this problem , any angle may be divided into four , eight , sixteen , & c . equal angles .. • Prop . x . A ...
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 angle ACB angle BAC angle equal Apply Euc base BC bisects the angle chord circle cutting circle described circle whose center circles touch circumscribing circle construction describe a circle diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Euclid exterior angle Geometrical given angle given circle given line given point given straight line given triangle greater hypotenuse inscribed circle isosceles triangle Let ABC line joining lines be drawn locus magnitudes meet the circumference opposite sides parallel to BC parallelogram parallelopiped pentagon perpendicular plane point of contact polygon Prop PROPOSITION proved quadrilateral figure radius rectangle contained right angles right-angled triangle segment semicircle shew shewn side BC similar triangles solid angle square on AC tangent THEOREM touch the circle trapezium triangle ABC vertex vertical angle Whence 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.