The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Libro 11853 |
Dentro del libro
Resultados 1-5 de 44
Página 6
... ways , do not meet . XXXVI . A parallelogram is a four - sided figure which has its opposite sides parallel ; and each of the two straight lines drawn joining the two pairs of opposite angular 6 [ BOOK THE ELEMENTS OF EUCLID .
... ways , do not meet . XXXVI . A parallelogram is a four - sided figure which has its opposite sides parallel ; and each of the two straight lines drawn joining the two pairs of opposite angular 6 [ BOOK THE ELEMENTS OF EUCLID .
Página 7
Euclides Henry Judge Hose. straight lines drawn joining the two pairs of opposite angular points , is called a diagonal of the parallel- ogram . OBS . In the figure the parallelogram is denoted either by ABCD , or by AC , or by BD ; AC ...
Euclides Henry Judge Hose. straight lines drawn joining the two pairs of opposite angular points , is called a diagonal of the parallel- ogram . OBS . In the figure the parallelogram is denoted either by ABCD , or by AC , or by BD ; AC ...
Página 39
... pairs of equal angles , be equal ; ac being opposite to the angle ABC , and DF to the angle DEF . Then these two triangles shall be equal in every respect , i . e . ( 1 ) the third angle BAC shall be equal to the third angle EDF ; ( 2 ) ...
... pairs of equal angles , be equal ; ac being opposite to the angle ABC , and DF to the angle DEF . Then these two triangles shall be equal in every respect , i . e . ( 1 ) the third angle BAC shall be equal to the third angle EDF ; ( 2 ) ...
Página 40
... pair of alternate angles equal to one another : then these two straight lines shall be pa- rallel . Let EF , cutting the two straight lines Ab , cd in G , н , make the pair of alter- nate angles AGH , GHD equal to one another . Then AB ...
... pair of alternate angles equal to one another : then these two straight lines shall be pa- rallel . Let EF , cutting the two straight lines Ab , cd in G , н , make the pair of alter- nate angles AGH , GHD equal to one another . Then AB ...
Página 41
... pair of alternate angles equal , ab , CD are parallel . Which was to be proved . PROP . XXVIII . THEOR . If a straight line cutting two other straight lines make one of the exterior angles equal to the interior and opposite angle on the ...
... pair of alternate angles equal , ab , CD are parallel . Which was to be proved . PROP . XXVIII . THEOR . If a straight line cutting two other straight lines make one of the exterior angles equal to the interior and opposite angle on the ...
Términos y frases comunes
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
Pasajes populares
Página 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...
Página 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.
Página 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.