Eucharist question

Is this quote from Nicholas II's Roman synod of 1059 actual Catholic doctrine:

of course

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So the dragon was enraged with the woman, and went off to make war with the rest of her children, who keep the commandments of God and hold to the testimony of Jesus.

From the Catechism of the Catholic Church:

1373 "Christ Jesus, who died, yes, who was raised from the dead, who is at the right hand of God, who indeed intercedes for us," is present in many ways to his Church: in his word, in his Church's prayer, "where two or three are gathered in my name,"in the poor, the sick, and the imprisoned,in the sacraments of which he is the author, in the sacrifice of the Mass, and in the person of the minister. But "he is present . . . most especially in the Eucharistic species."
1374 The mode of Christ's presence under the Eucharistic species is unique. It raises the Eucharist above all the sacraments as "the perfection of the spiritual life and the end to which all the sacraments tend." In the most blessed sacrament of the Eucharist "the body and blood, together with the soul and divinity, of our Lord Jesus Christ and, therefore, the whole Christ is truly, really, and substantially contained." "This presence is called 'real' - by which is not intended to exclude the other types of presence as if they could not be 'real' too, but because it is presence in the fullest sense: that is to say, it is a substantial presence by which Christ, God and man, makes himself wholly and entirely present."
1375 It is by the conversion of the bread and wine into Christ's body and blood that Christ becomes present in this sacrament. The Church Fathers strongly affirmed the faith of the Church in the efficacy of the Word of Christ and of the action of the Holy Spirit to bring about this conversion. Thus St. John Chrysostom declares:

It is not man that causes the things offered to become the Body and Blood of Christ, but he who was crucified for us, Christ himself. The priest, in the role of Christ, pronounces these words, but their power and grace are God's. This is my body, he says. This word transforms the things offered.

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"Go and learn what this means, 'I desire mercy, not sacrifice.' For I have come to call not the righteous but sinners." -- Matthew 9:13

Of course it is. The Eucharist is truly the Body and Blood of Christ.

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Here at my path's end I am lingering / In deep darkness buried / Beyond towers strong and high / Beyond all mountains steep

Above all shadows rides the sun / And stars always dwell / I will not say, "The day is done" / or to the stars, "Farewell."

It's this bit that gets me.

"Sensibly" deals with the realm of accidents.

As for "reality", this seems to relate to the medieval contrast between res and sacramentum. The res of the Eucharist is, however, substantial... it always seemed to me that the physical integrity of the eucharistic elements was a matter of accidents rather than substance; ie that each particle of the host was the whole Christ. How can this whole Christ be broken in substance?

I think that it's just that teachers have to try and explain difficult concepts for some to understand in a context that the immidiate audience can comprehend. I think that words used in another part of the world, at a past time on earth, in a foreign culture may not resonate or be comprehended as well as it may have been in the place and time that it was spoken at, compared to a modern time of today and a student of today?

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So the dragon was enraged with the woman, and went off to make war with the rest of her children, who keep the commandments of God and hold to the testimony of Jesus.