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 20
... bisect a given angle , i . e . to divide it into two equal angles . Let BAC be the given angle . It is required to bisect the angle ABC , i . e . to divide it into two equal angles . In AB take any point D ; and from AC 20 [ воок THE ...
... bisect a given angle , i . e . to divide it into two equal angles . Let BAC be the given angle . It is required to bisect the angle ABC , i . e . to divide it into two equal angles . In AB take any point D ; and from AC 20 [ воок THE ...
Página 21
... bisected by the straight line Af . Which was to be done . PROP . X. PROB . To bisect a given finite straight line , i . e . to divide it into two equal parts . Let AB be the given finite straight line . It is required to bisect AB , i ...
... bisected by the straight line Af . Which was to be done . PROP . X. PROB . To bisect a given finite straight line , i . e . to divide it into two equal parts . Let AB be the given finite straight line . It is required to bisect AB , i ...
Página 23
... circle cuts AB , or AB produced if necessary ; bisect ( i . 10 ) Gн in K , and join сK . Then CK shall be perpendicular to AB . Join co and сH . A E G F H K B D Because CG is equal to CH by the def " 1. ] 23 PROPOSITIONS XI . XII .
... circle cuts AB , or AB produced if necessary ; bisect ( i . 10 ) Gн in K , and join сK . Then CK shall be perpendicular to AB . Join co and сH . A E G F H K B D Because CG is equal to CH by the def " 1. ] 23 PROPOSITIONS XI . XII .
Página 28
... Bisect ( i . 10 ) AC in E , and join BE . Produce BE to F ; from EF cut off ( i . 3 ) EG equal to EB ; and join co . E C D Because by const " AE is equal B to EC , and BE to EG , and the angle AEB is equal to the angle CEG , since they ...
... Bisect ( i . 10 ) AC in E , and join BE . Produce BE to F ; from EF cut off ( i . 3 ) EG equal to EB ; and join co . E C D Because by const " AE is equal B to EC , and BE to EG , and the angle AEB is equal to the angle CEG , since they ...
Página 29
Euclides Henry Judge Hose. Produce AC to H ; bisect ( i . 10 ) вo in K , and join AK . Produce AK to L ; from KL cut off ( i . 3 ) KM equal to KA ; and join Cм . K C D By const BK is equal to KC , and AK to KM , and the angle AKB is B ...
Euclides Henry Judge Hose. Produce AC to H ; bisect ( i . 10 ) вo in K , and join AK . Produce AK to L ; from KL cut off ( i . 3 ) KM equal to KA ; and join Cм . K C D By const BK is equal to KC , and AK to KM , and the angle AKB is B ...
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.