The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Libro 11853 |
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Página 4
... divided by the diameter . XIX . This definition is the same as Bk . iii . Def . 6 . XX . When the lines which contain a plane figure are all straight lines , it is called a rectilinear figure , and the straight lines are called its ...
... divided by the diameter . XIX . This definition is the same as Bk . iii . Def . 6 . XX . When the lines which contain a plane figure are all straight lines , it is called a rectilinear figure , and the straight lines are called its ...
Página 21
... ) ; and hence the base AD is equal to the base DB . Hence the straight line AB is divided into two equal parts , or bisected in the point D. Which was to be done . PROP . XI . PROB . To draw a straight 1. ] 21 PROPOSITIONS IX . X.
... ) ; and hence the base AD is equal to the base DB . Hence the straight line AB is divided into two equal parts , or bisected in the point D. Which was to be done . PROP . XI . PROB . To draw a straight 1. ] 21 PROPOSITIONS IX . X.
Página 61
... given angle & . Which was to be done . II . Let the polygon have more than four sides . The polygon must be divided into triangles by joining G one of its angular points with all the others ; 1. ] 61 PROPOSITION XLV .
... given angle & . Which was to be done . II . Let the polygon have more than four sides . The polygon must be divided into triangles by joining G one of its angular points with all the others ; 1. ] 61 PROPOSITION XLV .
Página 68
... divided into any number of parts : then the rectangle contained by the two straight lines shall be equal to the rectangles contained by the undivided and the several parts of the divided line . Let A and BC be two straight lines , and ...
... divided into any number of parts : then the rectangle contained by the two straight lines shall be equal to the rectangles contained by the undivided and the several parts of the divided line . Let A and BC be two straight lines , and ...
Página 69
... divided into any two parts : then the rectangles contained by the whole line and each of the parts shall be together equal to the square of the whole line . Let the straight line AB be divided into any two parts in c . Then the ...
... divided into any two parts : then the rectangles contained by the whole line and each of the parts shall be together equal to the square of the whole line . Let the straight line AB be divided into any two parts in c . Then 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.