## A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ... |

### From inside the book

Results 1-5 of 5

Page 3

A

contemplatively ; or , it proposes something to be done , problematically or

mechanically . A CONVERSE

which ...

A

**PROPOSITION**is either a Theorem , proposed to be proved or demonstrated ,contemplatively ; or , it proposes something to be done , problematically or

mechanically . A CONVERSE

**PROPOSITION**is the contrary of the other ; that ,which ...

Page 27

Pr.i. or 2. & c . Refers to the first or second Problem , for the constructing of some

Figure , & c . P. 1. or 2. & c . Refers to the first or second

for proof of the Affertion . & c . To the second

Pr.i. or 2. & c . Refers to the first or second Problem , for the constructing of some

Figure , & c . P. 1. or 2. & c . Refers to the first or second

**Proposition**of that Book ,for proof of the Affertion . & c . To the second

**Proposition**of the third Book . ' C. 2. Page 257

The fourteenth

, if the Antecedent of one Ratio be greater than the Antecedent of the other , the

Consequent of the first is also greater than the Consequent of the other ; if the ...

The fourteenth

**Proposition**of Euclid . A B If four Quantities are proportional ; then, if the Antecedent of one Ratio be greater than the Antecedent of the other , the

Consequent of the first is also greater than the Consequent of the other ; if the ...

Page 269

Professor Simson is aware of that deficiency , and has very judiciously introduced

it , as an additional

the Converse of divided Ratio ( E ) unless he had , also , given the Converse of ...

Professor Simson is aware of that deficiency , and has very judiciously introduced

it , as an additional

**Proposition**( B ; ) after which , I must think it needless , to addthe Converse of divided Ratio ( E ) unless he had , also , given the Converse of ...

Page 308

SHOL : This

Pythagorean

of the firs , of these Elements , universally . Seeing , by Th.10 . of this 6th Book it is

...

SHOL : This

**Proposition**, by the Doctrine of Proportion , extends the famousPythagorean

**Proposition**, viz . the 47th of the first Book of Euclid , and the 20th ,of the firs , of these Elements , universally . Seeing , by Th.10 . of this 6th Book it is

...

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### Common terms and phrases

ABCD added alſo Altitudes analogous Area Baſe becauſe biſected Book called Center Chord Circle Circumference common Cone conf conſequently Conſtruction contained cuting Cylinder Demonſtration deſcribe Diagonal Diameter difference divided draw drawn equal Euclid evident extreme fame Feet Figure firſt formed four fourth given given Line greater half Hence Inches inſcribed join laſt leſs manner mean meaſure multiplied muſt oppoſite parallel Parallelogram Parallelopiped Pentagon perpendicular Plane Point Poligon Priſm Prob PROBLEM produced Proportion Propoſition proved Pyramid Quantities Radius Ratio Rect Rectangle reſpectively Right Angles Right Line ſame ſame Ratio ſay ſeeing Segment Sides ſimilar Solid ſome Sphere Square ſuch Surface taken Terms THEOREM third thoſe touch Triangle uſe wherefore whole whoſe

### Popular passages

Page 124 - When you have proved that the three angles of every triangle are equal to two right angles...

Page 221 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 285 - EG, let fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter DS, EF (p.

Page 284 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Page 186 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two; and when the adjacent angles are equal, they are right angles.

Page 248 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 161 - In any triangle, if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base.

Page 160 - In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base.

Page 250 - Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F.

Page 124 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.