Elements of geometry, based on Euclid, books i-iii1876 - 119 σελίδες |
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Αποτελέσματα 1 - 5 από τα 51.
Σελίδα 6
Edward Atkins. Thus , the angle contained by the straight lines AB and BC is ... equal to one another , each of the angles is called a right angle ; and the ... equal to one another . 16. And this point is called the centre of the circle ...
Edward Atkins. Thus , the angle contained by the straight lines AB and BC is ... equal to one another , each of the angles is called a right angle ; and the ... equal to one another . 16. And this point is called the centre of the circle ...
Σελίδα 10
... BC = AB . AC and BC each = AB . AC = BC . ... AB = BC = CA . The sign signifies " is greater than , " and " is less ... equal to AB ( Def . 15 ) . Because the point B is the centre of the circle ACE , BC is equal to BA ( Def . 15 ) ...
... BC = AB . AC and BC each = AB . AC = BC . ... AB = BC = CA . The sign signifies " is greater than , " and " is less ... equal to AB ( Def . 15 ) . Because the point B is the centre of the circle ACE , BC is equal to BA ( Def . 15 ) ...
Σελίδα 11
... BC the given straight line . It is required to draw from the point A a straight line equal to BC . CONSTRUCTION . From the point A to B draw the straight Draw AB . line AB ( Post . 1 ) . Upon AB describe the equilateral triangle DAB ...
... BC the given straight line . It is required to draw from the point A a straight line equal to BC . CONSTRUCTION . From the point A to B draw the straight Draw AB . line AB ( Post . 1 ) . Upon AB describe the equilateral triangle DAB ...
Σελίδα 12
... equal to C , the less . A as centre and radius AD . A B B CONSTRUCTION . From the point A draw the straight line AD ... BC shall be equal to the base EF ; AA The triangle ABC shall be equal to the triangle DEF ; * Q. E. F. is an ...
... equal to C , the less . A as centre and radius AD . A B B CONSTRUCTION . From the point A draw the straight line AD ... BC shall be equal to the base EF ; AA The triangle ABC shall be equal to the triangle DEF ; * Q. E. F. is an ...
Σελίδα 13
... equal , each to each , viz . , the angle ABC to the angle DEF , and the angle ACB to the angle DFE . PROOF . For if ... BC shall coincide with the base EF . Because the point B coinciding with E , and C with F , if the base BC do not ...
... equal , each to each , viz . , the angle ABC to the angle DEF , and the angle ACB to the angle DFE . PROOF . For if ... BC shall coincide with the base EF . Because the point B coinciding with E , and C with F , if the base BC do not ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Based on Euclid, Βιβλία 1-3 Edward Atkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal AC and CD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle contained angle DEF angle EDF angle equal angles BGH angles CBA base BC BC is equal bisect centre circle ABC circumference diagonal diameter double draw equal circles equal to AC equal to twice EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line gnomon greater interior and opposite isosceles triangle less Let ABC Let the straight opposite angles parallel to BC parallelogram perpendicular produced PROOF PROOF.-Because Q.E.D. Proposition rectangle AD rectangle AE rectangle contained remaining angle right angle Const right angles Ax segment semicircle side BC square described square on AC touches the circle triangle ABC triangle DEF twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 37 - 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.
Σελίδα 13 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC be produced to D and E.
Σελίδα 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 17 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 53 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Σελίδα 9 - If a straight line meet 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 71 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Σελίδα 34 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Σελίδα 69 - 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.