The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 páginas |
Dentro del libro
Resultados 1-5 de 31
Página 10
... fore , because in the triangles DBC , ACB , DB is A D equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , Cв , each to each ; and the angle DBC is equal to the angle ACB ( Hyp . ) ; therefore the base ...
... fore , because in the triangles DBC , ACB , DB is A D equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , Cв , each to each ; and the angle DBC is equal to the angle ACB ( Hyp . ) ; therefore the base ...
Página 12
... fore the base AD is equal to the base ( 1. 4. ) DB , and the straight line AB is divided into two equal parts in the point D. done . Which was to be C A D B PROP . XI . PROB . To draw a straight 12 EUCLID'S ELEMENTS .
... fore the base AD is equal to the base ( 1. 4. ) DB , and the straight line AB is divided into two equal parts in the point D. done . Which was to be C A D B PROP . XI . PROB . To draw a straight 12 EUCLID'S ELEMENTS .
Página 14
... fore the angles CBE , EBD are two right angles ( Def . 10. ) ; and because CBE IS equal to the two angles CBA , ABE to- gether , add the angle EBD to each of D B C D в C these equals ; therefore the angles CBE , EBD are equal ( Ax . 2 ...
... fore the angles CBE , EBD are two right angles ( Def . 10. ) ; and because CBE IS equal to the two angles CBA , ABE to- gether , add the angle EBD to each of D B C D в C these equals ; therefore the angles CBE , EBD are equal ( Ax . 2 ...
Página 18
... In the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . There- fore any two sides , & c . Q. E.D. PROP . XXI . THEOR , If , from the 18 EUCLID'S ELEMENTS .
... In the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . There- fore any two sides , & c . Q. E.D. PROP . XXI . THEOR , If , from the 18 EUCLID'S ELEMENTS .
Página 21
... fore greater than the side EF ; but EG is equal to BC ; and therefore also BC is greater than EF . Therefore , if two triangles , & c . Q.E.D. PROP . XXV . THEOR . If two triangles have two sides of the one equal to two sides of the ...
... fore greater than the side EF ; but EG is equal to BC ; and therefore also BC is greater than EF . Therefore , if two triangles , & c . Q.E.D. PROP . XXV . THEOR . If two triangles have two sides of the one equal to two sides of the ...
Otras ediciones - Ver todas
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Sin vista previa disponible - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Sin vista previa disponible - 2014 |
Términos y frases comunes
ABCD adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles CAB base BC BC is equal bisect centre circle ABC circumference diameter divided double draw a straight equal angles equal circles equal straight lines equal to FB exterior angle fore given point given rectilineal angle given straight line gnomon greater half a right hypotenuse isosceles triangle less Let ABC Let the straight line be drawn opposite angles parallel parallelogram perpendicular PROB produced Q. E. D. PROP rectangle AE rectangle contained rectilineal figure remaining angle right angles segment semicircle side BC square of AC straight line AC straight line drawn THEOR touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle
Pasajes populares
Página 6 - If a straight line meets 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 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 20 - If two triangles have two sides of the one equal to two sides of the...
Página 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Página 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.
Página 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.
Página 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
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 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.
Página 7 - 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.