The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Bücher 11853 |
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Seite 22
... coincides with one of them , as B ( Fig . 2 ) . F F C D C E B A D B E G Fig . 1 . Fig . 2 . If c lie between A and B , in AC take any point D , and from CB , or CB produced if necessary , cut off ( i . 3 ) CE equal to CD ; or if c coincide ...
... coincides with one of them , as B ( Fig . 2 ) . F F C D C E B A D B E G Fig . 1 . Fig . 2 . If c lie between A and B , in AC take any point D , and from CB , or CB produced if necessary , cut off ( i . 3 ) CE equal to CD ; or if c coincide ...
Seite 50
... mon base BC , are terminated in the same point or are not . I. Let the sides AD , EF be termi- nated in the same point ; the ex- B C D E tremity D of AD coinciding with the extremity E of 50 [ воок THE ELEMENTS OF EUCLID .
... mon base BC , are terminated in the same point or are not . I. Let the sides AD , EF be termi- nated in the same point ; the ex- B C D E tremity D of AD coinciding with the extremity E of 50 [ воок THE ELEMENTS OF EUCLID .
Seite 51
Euclides Henry Judge Hose. tremity D of AD coinciding with the extremity E of EF . Since BD is one of the diagonals of the parallelogram ABCD , it bisects ( i . 34 ) it : therefore the parallelogram ABCD is double of the triangle BDC ...
Euclides Henry Judge Hose. tremity D of AD coinciding with the extremity E of EF . Since BD is one of the diagonals of the parallelogram ABCD , it bisects ( i . 34 ) it : therefore the parallelogram ABCD is double of the triangle BDC ...
Seite 84
... coincide with AC , E either falling in BC ( Fig . 1 ) , or in CD without BC ( Fig . 2 ) . Because BC is divided into two parts in E ( Fig . 1 ) , or because BE is divided into two parts in c ( Fig . 2 ) , there- fore in both figures the ...
... coincide with AC , E either falling in BC ( Fig . 1 ) , or in CD without BC ( Fig . 2 ) . Because BC is divided into two parts in E ( Fig . 1 ) , or because BE is divided into two parts in c ( Fig . 2 ) , there- fore in both figures the ...
Seite 85
... coincide with AC , E and c being one and the same point . B A E C Then , because ACB is a right angle , the square of AB is equal to the squares of AC , CB . To each of these equals add the square of BC ; then the squares of AB , BC are ...
... coincide with AC , E and c being one and the same point . B A E C Then , because ACB is a right angle , the square of AB is equal to the squares of AC , CB . To each of these equals add the square of BC ; then the squares of AB , BC are ...
Häufige Begriffe und Wortgruppen
ABC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles are equal angular points base BC bisected centre circle ABC circle DEF circumference const cut the circle diagonal draw equal angles equal Ax equals add equi equimultiples exterior angle FGHKL fore four magnitudes fourth given straight line gnomon hence the angle homologous hyps included angle interior and opposite join less Let ABC multiple opposite angle parallelogram perpendicular produced PROP proportional proved radius rectangle contained remaining angle respectively equal right angles segment shewn sides BC similar solid angle square of AC THEOR thing are equal third angle three angles touching the circle triangle ABC unequal
Beliebte Passagen
Seite 39 - 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...
Seite 52 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Seite 5 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw, from the point A, a straight line equal to BC.
Seite 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.
Seite 105 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Seite 118 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Seite 66 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 6 - 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.
Seite 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.