Elements of geometry, based on Euclid, books i-iii1876 - 119 páginas |
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Página 7
... semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . 19. A segment of a circle is the figure contained by a straight line and the part of the circumference which it cuts off . 20 ...
... semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . 19. A segment of a circle is the figure contained by a straight line and the part of the circumference which it cuts off . 20 ...
Página 75
... semicircle BHF ; Produce DE to H , and join GH ; Then the square described upon EH shall be equal to the rectilineal figure A. PROOF . Because the straight line BF is divided into two equal parts in the point G , and into two unequal ...
... semicircle BHF ; Produce DE to H , and join GH ; Then the square described upon EH shall be equal to the rectilineal figure A. PROOF . Because the straight line BF is divided into two equal parts in the point G , and into two unequal ...
Página 98
... semicircle . CONSTRUCTION . - Take F , the centre of the circle ABCD ( III . 1 ) , and join BF , DF . PROOF . - Because the angle BFD is at the centre , and the angle BAD at the circum- ference , and that they have the same arc for ...
... semicircle . CONSTRUCTION . - Take F , the centre of the circle ABCD ( III . 1 ) , and join BF , DF . PROOF . - Because the angle BFD is at the centre , and the angle BAD at the circum- ference , and that they have the same arc for ...
Página 99
... semicircle . CONSTRUCTION . - Draw AF to the centre , and produce it to C , and join CE . PROOF . Then the segment BADC is B also = 24 BED . .. 4 BAD = 4 BED . greater than a semicircle , and therefore the angles BAC , 4 BAC = BEC in it ...
... semicircle . CONSTRUCTION . - Draw AF to the centre , and produce it to C , and join CE . PROOF . Then the segment BADC is B also = 24 BED . .. 4 BAD = 4 BED . greater than a semicircle , and therefore the angles BAC , 4 BAC = BEC in it ...
Página 107
... semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle . Let ABC be a circle , of which BC is a diameter , and E the centre ; and draw CA , dividing the circle into the ...
... semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle . Let ABC be a circle , of which BC is a diameter , and E the centre ; and draw CA , dividing the circle into the ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 17 - If two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.